Gunning, Robert C. (Robert Clifford) 1931
Overview
Works:  97 works in 470 publications in 5 languages and 8,605 library holdings 

Genres:  Conference papers and proceedings 
Roles:  Author, Editor, Author of introduction, Honoree, Other, win 
Publication Timeline
.
Most widely held works about
Robert C Gunning
 Gunning, Robert Clifford : complex analysis( )
 Office of Dean of the Faculty Records by Princeton University( )
Most widely held works by
Robert C Gunning
Lectures on Riemann surfaces, Jacobi varieties by
Robert Clifford Gunning(
)
20 editions published between 1972 and 2015 in English and held by 1,069 WorldCat member libraries worldwide
A sequel to Lectures on Riemann Surfaces (Mathematical Notes, 1966), this volume continues the discussion of the dimensions of spaces of holomorphic crosssections of complex line bundles over compact Riemann surfaces. Whereas the earlier treatment was limited to results obtainable chiefly by onedimensional methods, the more detailed analysis presented here requires the use of various properties of Jacobi varieties and of symmetric products of Riemann surfaces, and so serves as a further introduction to these topics as well. The first chapter consists of a rather explicit description of a canonical basis for the Abelian differentials on a marked Riemann surface, and of the description of the canonical meromorphic differentials and the prime function of a marked Riemann surface. Chapter 2 treats Jacobi varieties of compact Riemann surfaces and various subvarieties that arise in determining the dimensions of spaces of holomorphic crosssections of complex line bundles. In Chapter 3, the author discusses the relations between Jacobi varieties and symmetric products of Riemann surfaces relevant to the determination of dimensions of spaces of holomorphic crosssections of complex line bundles. The final chapter derives Torelli's theorem following A. Weil, but in an analytical context. Originally published in 1973. The Princeton Legacy Library uses the latest printondemand technology to again make available previously outofprint books from the distinguished backlist of Princeton University Press. These paperback editions preserve the original texts of these important books while presenting them in durable paperback editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905
20 editions published between 1972 and 2015 in English and held by 1,069 WorldCat member libraries worldwide
A sequel to Lectures on Riemann Surfaces (Mathematical Notes, 1966), this volume continues the discussion of the dimensions of spaces of holomorphic crosssections of complex line bundles over compact Riemann surfaces. Whereas the earlier treatment was limited to results obtainable chiefly by onedimensional methods, the more detailed analysis presented here requires the use of various properties of Jacobi varieties and of symmetric products of Riemann surfaces, and so serves as a further introduction to these topics as well. The first chapter consists of a rather explicit description of a canonical basis for the Abelian differentials on a marked Riemann surface, and of the description of the canonical meromorphic differentials and the prime function of a marked Riemann surface. Chapter 2 treats Jacobi varieties of compact Riemann surfaces and various subvarieties that arise in determining the dimensions of spaces of holomorphic crosssections of complex line bundles. In Chapter 3, the author discusses the relations between Jacobi varieties and symmetric products of Riemann surfaces relevant to the determination of dimensions of spaces of holomorphic crosssections of complex line bundles. The final chapter derives Torelli's theorem following A. Weil, but in an analytical context. Originally published in 1973. The Princeton Legacy Library uses the latest printondemand technology to again make available previously outofprint books from the distinguished backlist of Princeton University Press. These paperback editions preserve the original texts of these important books while presenting them in durable paperback editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905
Lectures on complex analytic varieties: finite analytic mappings by
Robert Clifford Gunning(
)
24 editions published between 1974 and 2016 in English and Undetermined and held by 1,007 WorldCat member libraries worldwide
This book is a sequel to Lectures on Complex Analytic Varieties: The Local Paranwtrization Theorem (Mathematical Notes 10, 1970). Its unifying theme is the study of local properties of finite analytic mappings between complex analytic varieties; these mappings are those in several dimensions that most closely resemble general complex analytic mappings in one complex dimension. The purpose of this volume is rather to clarify some algebraic aspects of the local study of complex analytic varieties than merely to examine finite analytic mappings for their own sake. Originally published in 1974. The Princeton Legacy Library uses the latest printondemand technology to again make available previously outofprint books from the distinguished backlist of Princeton University Press. These paperback editions preserve the original texts of these important books while presenting them in durable paperback editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905
24 editions published between 1974 and 2016 in English and Undetermined and held by 1,007 WorldCat member libraries worldwide
This book is a sequel to Lectures on Complex Analytic Varieties: The Local Paranwtrization Theorem (Mathematical Notes 10, 1970). Its unifying theme is the study of local properties of finite analytic mappings between complex analytic varieties; these mappings are those in several dimensions that most closely resemble general complex analytic mappings in one complex dimension. The purpose of this volume is rather to clarify some algebraic aspects of the local study of complex analytic varieties than merely to examine finite analytic mappings for their own sake. Originally published in 1974. The Princeton Legacy Library uses the latest printondemand technology to again make available previously outofprint books from the distinguished backlist of Princeton University Press. These paperback editions preserve the original texts of these important books while presenting them in durable paperback editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905
Analytic functions of several complex variables by
R. C Gunning(
Book
)
48 editions published between 1965 and 2012 in 3 languages and held by 745 WorldCat member libraries worldwide
The theory of analytic functions of several complex variables enjoyed a period of remarkable development in the middle part of the twentieth century. After initial successes by Poincaré and others in the late 19th and early 20th centuries, the theory encountered obstacles that prevented it from growing quickly into an analogue of the theory for functions of one complex variable. Beginning in the 1930s, initially through the work of Oka, then H. Cartan, and continuing with the work of Grauert, Remmert, and others, new tools were introduced into the theory of several complex variables that resol
48 editions published between 1965 and 2012 in 3 languages and held by 745 WorldCat member libraries worldwide
The theory of analytic functions of several complex variables enjoyed a period of remarkable development in the middle part of the twentieth century. After initial successes by Poincaré and others in the late 19th and early 20th centuries, the theory encountered obstacles that prevented it from growing quickly into an analogue of the theory for functions of one complex variable. Beginning in the 1930s, initially through the work of Oka, then H. Cartan, and continuing with the work of Grauert, Remmert, and others, new tools were introduced into the theory of several complex variables that resol
Lectures on modular forms by
Robert C Gunning(
Book
)
22 editions published between 1959 and 2016 in English and Undetermined and held by 740 WorldCat member libraries worldwide
New interest in modular forms of one complex variable has been caused chiefly by the work of Selberg and of Eichler. But there has been no introductory work covering the background of these developments. H.C. Gunning's book surveys techniques and problems; only the simpler cases are treatedmodular forms of even weights without multipliers, the principal congruence subgroups, and the Hecke operators for the full modular group alone
22 editions published between 1959 and 2016 in English and Undetermined and held by 740 WorldCat member libraries worldwide
New interest in modular forms of one complex variable has been caused chiefly by the work of Selberg and of Eichler. But there has been no introductory work covering the background of these developments. H.C. Gunning's book surveys techniques and problems; only the simpler cases are treatedmodular forms of even weights without multipliers, the principal congruence subgroups, and the Hecke operators for the full modular group alone
Problems in analysis: a symposium in honor of Salomon Bochner by
R. C Gunning(
Book
)
25 editions published between 1970 and 2015 in English and Italian and held by 739 WorldCat member libraries worldwide
The present volume reflects both the diversity of Bochner's pursuits in pure mathematics and the influence his example and thought have had upon contemporary researchers. Originally published in 1971. The Princeton Legacy Library uses the latest printondemand technology to again make available previously outofprint books from the distinguished backlist of Princeton University Press. These paperback editions preserve the original texts of these important books while presenting them in durable paperback editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905
25 editions published between 1970 and 2015 in English and Italian and held by 739 WorldCat member libraries worldwide
The present volume reflects both the diversity of Bochner's pursuits in pure mathematics and the influence his example and thought have had upon contemporary researchers. Originally published in 1971. The Princeton Legacy Library uses the latest printondemand technology to again make available previously outofprint books from the distinguished backlist of Princeton University Press. These paperback editions preserve the original texts of these important books while presenting them in durable paperback editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905
On uniformization of complex manifolds : the role of connections by
R. C Gunning(
Book
)
23 editions published between 1978 and 2016 in English and held by 689 WorldCat member libraries worldwide
The classical uniformization theorem for Riemann surfaces and its recent extensions can be viewed as introducing special pseudogroup structures, affine or projective structures, on Riemann surfaces. In fact, the additional structures involved can be considered as local forms of the uniformizations of Riemann surfaces. In this study, Robert Gunning discusses the corresponding pseudogroup structures on higherdimensional complex manifolds, modeled on the theory as developed for Riemann surfaces. Originally published in 1978. The Princeton Legacy Library uses the latest printondemand technology to again make available previously outofprint books from the distinguished backlist of Princeton University Press. These paperback editions preserve the original texts of these important books while presenting them in durable paperback editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905
23 editions published between 1978 and 2016 in English and held by 689 WorldCat member libraries worldwide
The classical uniformization theorem for Riemann surfaces and its recent extensions can be viewed as introducing special pseudogroup structures, affine or projective structures, on Riemann surfaces. In fact, the additional structures involved can be considered as local forms of the uniformizations of Riemann surfaces. In this study, Robert Gunning discusses the corresponding pseudogroup structures on higherdimensional complex manifolds, modeled on the theory as developed for Riemann surfaces. Originally published in 1978. The Princeton Legacy Library uses the latest printondemand technology to again make available previously outofprint books from the distinguished backlist of Princeton University Press. These paperback editions preserve the original texts of these important books while presenting them in durable paperback editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905
Riemann surfaces and generalized theta functions by
Robert C Gunning(
Book
)
12 editions published in 1976 in English and held by 430 WorldCat member libraries worldwide
12 editions published in 1976 in English and held by 430 WorldCat member libraries worldwide
Lectures on vector bundles over Riemann surfaces by
Robert C Gunning(
Book
)
11 editions published in 1967 in English and Italian and held by 424 WorldCat member libraries worldwide
11 editions published in 1967 in English and Italian and held by 424 WorldCat member libraries worldwide
Lectures on Riemann surfaces by
R. C Gunning(
Book
)
23 editions published between 1966 and 2016 in 3 languages and held by 405 WorldCat member libraries worldwide
23 editions published between 1966 and 2016 in 3 languages and held by 405 WorldCat member libraries worldwide
Lectures on complex analytic varieties: the local parametrization theorem by
Robert Clifford Gunning(
Book
)
15 editions published in 1970 in English and held by 384 WorldCat member libraries worldwide
15 editions published in 1970 in English and held by 384 WorldCat member libraries worldwide
Theta functions, Bowdoin 1987 by
Summer Research Institute on Theta Functions(
Book
)
22 editions published between 1989 and 2012 in English and held by 367 WorldCat member libraries worldwide
22 editions published between 1989 and 2012 in English and held by 367 WorldCat member libraries worldwide
Modern methods in complex analysis(
Book
)
9 editions published between 1995 and 1996 in English and held by 304 WorldCat member libraries worldwide
9 editions published between 1995 and 1996 in English and held by 304 WorldCat member libraries worldwide
Introduction to holomorphic functions of several variables by
Robert Clifford Gunning(
Book
)
7 editions published between 1990 and 2017 in English and held by 242 WorldCat member libraries worldwide
"Introduction to Holomorphlc Functions of SeveralVariables, Volumes 1111 provide an extensiveintroduction to the OkaCartan theory of holomorphicfunctions of several variables and holomorphicvarieties. Each volume covers a different aspect andcan be read independently."Provided by publisher
7 editions published between 1990 and 2017 in English and held by 242 WorldCat member libraries worldwide
"Introduction to Holomorphlc Functions of SeveralVariables, Volumes 1111 provide an extensiveintroduction to the OkaCartan theory of holomorphicfunctions of several variables and holomorphicvarieties. Each volume covers a different aspect andcan be read independently."Provided by publisher
Collected papers of Salomon Bochner by
S Bochner(
Book
)
2 editions published in 1992 in English and held by 108 WorldCat member libraries worldwide
2 editions published in 1992 in English and held by 108 WorldCat member libraries worldwide
Introduction to holomorphic functions of several variables by
Robert C Gunning(
Book
)
17 editions published between 1990 and 2018 in English and held by 89 WorldCat member libraries worldwide
"Introduction to Holomorphlc Functions of SeveralVariables, Volumes 1111 provide an extensiveintroduction to the OkaCartan theory of holomorphicfunctions of several variables and holomorphicvarieties. Each volume covers a different aspect andcan be read independently."Provided by publisher
17 editions published between 1990 and 2018 in English and held by 89 WorldCat member libraries worldwide
"Introduction to Holomorphlc Functions of SeveralVariables, Volumes 1111 provide an extensiveintroduction to the OkaCartan theory of holomorphicfunctions of several variables and holomorphicvarieties. Each volume covers a different aspect andcan be read independently."Provided by publisher
Introduction to holomorphic functions of several variables by
Robert Clifford Gunning(
Book
)
17 editions published between 1990 and 2018 in English and held by 89 WorldCat member libraries worldwide
Introduction to Holomorphlc Functions of SeveralVariables, Volumes 1111 provide an extensiveintroduction to the OkaCartan theory of holomorphicfunctions of several variables and holomorphicvarieties. Each volume covers a different aspect andcan be read independently
17 editions published between 1990 and 2018 in English and held by 89 WorldCat member libraries worldwide
Introduction to Holomorphlc Functions of SeveralVariables, Volumes 1111 provide an extensiveintroduction to the OkaCartan theory of holomorphicfunctions of several variables and holomorphicvarieties. Each volume covers a different aspect andcan be read independently
An introduction to analysis by
Robert C Gunning(
Book
)
6 editions published in 2018 in English and held by 64 WorldCat member libraries worldwide
An Introduction to Analysis is an essential primer on basic results in algebra, topology, and calculus for undergraduate students considering advanced degrees in mathematics. Ideal for use in a oneyear course, this unique textbook also introduces students to rigorous proofs and formal mathematical writing skills they need to excel. With a range of problems throughout, An Introduction to Analysis treats ndimensional calculus from the beginning (differentiation, the Riemann integral, series, and differential forms and Stokes's theorem) enabling students who are serious about mathematics to progress quickly to more challenging topics. The book discusses basic material on point set topology, such as normed and metric spaces, topological spaces, compact sets, and the Baire category theorem. It covers linear algebra as well, including vector spaces, linear mappings, Jordan normal form, bilinear mappings, and normal mappings
6 editions published in 2018 in English and held by 64 WorldCat member libraries worldwide
An Introduction to Analysis is an essential primer on basic results in algebra, topology, and calculus for undergraduate students considering advanced degrees in mathematics. Ideal for use in a oneyear course, this unique textbook also introduces students to rigorous proofs and formal mathematical writing skills they need to excel. With a range of problems throughout, An Introduction to Analysis treats ndimensional calculus from the beginning (differentiation, the Riemann integral, series, and differential forms and Stokes's theorem) enabling students who are serious about mathematics to progress quickly to more challenging topics. The book discusses basic material on point set topology, such as normed and metric spaces, topological spaces, compact sets, and the Baire category theorem. It covers linear algebra as well, including vector spaces, linear mappings, Jordan normal form, bilinear mappings, and normal mappings
Introduction to holomorphic functions of several variables by
Robert C Gunning(
Book
)
14 editions published in 1990 in English and held by 58 WorldCat member libraries worldwide
14 editions published in 1990 in English and held by 58 WorldCat member libraries worldwide
Riemann Surfaces and Generalized Theta Functions by
Robert C Gunning(
)
1 edition published in 1976 in English and held by 56 WorldCat member libraries worldwide
The investigation of the relationships between compact Riemann surfaces (al gebraic curves) and their associated complex tori (Jacobi varieties) has long been basic to the study both of Riemann surfaces and of complex tori. A Riemann surface is naturally imbedded as an analytic submanifold in its associated torus; and various spaces of linear equivalence elasses of divisors on the surface (or equivalently spaces of analytic equivalence elasses of complex line bundies over the surface), elassified according to the dimensions of the associated linear series (or the dimensions of the spaces of analytic crosssections), are naturally realized as analytic subvarieties of the associated torus. One of the most fruitful of the elassical approaches to this investigation has been by way of theta functions. The space of linear equivalence elasses of positive divisors of order g 1 on a compact connected Riemann surface M of genus g is realized by an irreducible (g 1)dimensional analytic subvariety, an irreducible hypersurface, of the associated gdimensional complex torus J(M); this hyper 1 surface W r;;;, J(M) is the image of the natural mapping Mg +J(M), and is g 1 1 birationally equivalent to the (g 1)fold symmetric product Mg jSgl of the Riemann surface M
1 edition published in 1976 in English and held by 56 WorldCat member libraries worldwide
The investigation of the relationships between compact Riemann surfaces (al gebraic curves) and their associated complex tori (Jacobi varieties) has long been basic to the study both of Riemann surfaces and of complex tori. A Riemann surface is naturally imbedded as an analytic submanifold in its associated torus; and various spaces of linear equivalence elasses of divisors on the surface (or equivalently spaces of analytic equivalence elasses of complex line bundies over the surface), elassified according to the dimensions of the associated linear series (or the dimensions of the spaces of analytic crosssections), are naturally realized as analytic subvarieties of the associated torus. One of the most fruitful of the elassical approaches to this investigation has been by way of theta functions. The space of linear equivalence elasses of positive divisors of order g 1 on a compact connected Riemann surface M of genus g is realized by an irreducible (g 1)dimensional analytic subvariety, an irreducible hypersurface, of the associated gdimensional complex torus J(M); this hyper 1 surface W r;;;, J(M) is the image of the natural mapping Mg +J(M), and is g 1 1 birationally equivalent to the (g 1)fold symmetric product Mg jSgl of the Riemann surface M
Vorlesungen über Riemannsche Flächen by
Robert C Gunning(
Book
)
2 editions published in 1972 in German and Multiple languages and held by 42 WorldCat member libraries worldwide
2 editions published in 1972 in German and Multiple languages and held by 42 WorldCat member libraries worldwide
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Related Identities
 Rossi, Hugo
 Bochner, S. (Salomon) 18991982 Honoree Author Dedicatee
 Ehrenpreis, Leon Other Editor
 American Mathematical Society Editor
 Bloom, Thomas Other
 Kohn, Joseph John 1932 Other
 Brumer, Armand Compiler Editor Scribe
 Cook, Mariana Author of introduction Author Photographer
 Moser, Hugo
 Farkas, Hershel M. Author Editor
Useful Links
Associated Subjects
Algebra Analytic continuation Analytic mappings Analytic spaces Approximation theory Bochner, S.(Salomon), Brown, J. Douglas(James Douglas), Calculus Canada College administrators Complex manifolds Connections (Mathematics) Education, Higher Education and state Educators Eisenhart, Luther Pfahler, Fiber bundles (Mathematics) Fine, Henry B.(Henry Burchard), Forms, Modular Functional analysis Functions, Theta Functions of complex variables Functions of several complex variables Global analysis (Mathematics) Group theory Holomorphic functions Jacobi varieties Knot theory Lester, Richard Allen, Magie, William Francis, Management Mathematical analysis Mathematics Modular functions Murray, James O.(James Ormsbee), New Jersey New JerseyPrinceton Palmer, R. R.(Robert Roswell), Princeton University Pseudogroups Riemann surfaces Root, Robert K.(Robert Kilburn), Scientists System analysis Topology United States Universities and collegesFaculty Winans, Samuel Ross,
Covers
Alternative Names
Ganning, R.
Ganning, R. 1931
Gunning, R. C.
Gunning, R.C. 1931
Gunning, R.C. (Robert Clifford), 1931
Gunning, Robert 1931
Gunning Robert C.
Gunning, Robert C., 1931
Gunning, Robert Clifford
Gunning, Robert Clifford 1931
Robert Gunning American mathematician
Robert Gunning Amerikaans wiskundige
Robert Gunning amerikansk matematikar
Robert Gunning amerikansk matematiker
Robert Gunning matemático estadounidense
Robert Gunning mathématicien américain
Robert Gunning USamerikanischer Mathematiker
Ганнинг Р.
ロバート・ガニング (数学者)
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