Shilov, G. E. (Georgiĭ Evgenʹevich)
Overview
Works:  183 works in 995 publications in 6 languages and 9,022 library holdings 

Genres:  Textbooks 
Roles:  Author, Editor, Creator, wpr, Other, Contributor 
Classifications:  QA331, 517.5 
Publication Timeline
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Most widely held works about
G. E Shilov
 The work of Silov on commutative semisimple Banach algebras by H Mirkil( Book )
 Verallgemeinerte Funktionen (Distributionen) by I. M Gelʹfand( Book )
Most widely held works by
G. E Shilov
An introduction to the theory of linear spaces by
G. E Shilov(
Book
)
37 editions published between 1961 and 2012 in English and Undetermined and held by 801 WorldCat member libraries worldwide
This introduction to linear algebra and functional analysis offers a clear expository treatment, viewing algebra, geometry, and analysis as parts of an integrated whole rather than separate subjects. All abstract ideas receive a high degree of motivation, and numerous examples illustrate many different fields of mathematics. Abundant problems include hints or answers
37 editions published between 1961 and 2012 in English and Undetermined and held by 801 WorldCat member libraries worldwide
This introduction to linear algebra and functional analysis offers a clear expository treatment, viewing algebra, geometry, and analysis as parts of an integrated whole rather than separate subjects. All abstract ideas receive a high degree of motivation, and numerous examples illustrate many different fields of mathematics. Abundant problems include hints or answers
Integral, measure and derivative : a unified approach by
G. E Shilov(
Book
)
45 editions published between 1965 and 1977 in English and held by 776 WorldCat member libraries worldwide
This treatment examines the general theory of the integral, Lebesque integral in nspace, the RiemannStieltjes integral, and more. The exposition is fresh and sophisticated, and will engage the interest of accomplished mathematicians.? SciTech Book News. 1966 edition
45 editions published between 1965 and 1977 in English and held by 776 WorldCat member libraries worldwide
This treatment examines the general theory of the integral, Lebesque integral in nspace, the RiemannStieltjes integral, and more. The exposition is fresh and sophisticated, and will engage the interest of accomplished mathematicians.? SciTech Book News. 1966 edition
Linear algebra by
G. E Shilov(
Book
)
35 editions published between 1971 and 2012 in English and Undetermined and held by 660 WorldCat member libraries worldwide
Covers determinants, linear spaces, systems of linear equations, linear functions of a vector argument, coordinate transformations, the canonical form of the matrix of a linear operator, bilinear and quadratic forms, Euclidean spaces, unitary spaces, quadratic forms in Euclidean and unitary spaces, finitedimensional space
35 editions published between 1971 and 2012 in English and Undetermined and held by 660 WorldCat member libraries worldwide
Covers determinants, linear spaces, systems of linear equations, linear functions of a vector argument, coordinate transformations, the canonical form of the matrix of a linear operator, bilinear and quadratic forms, Euclidean spaces, unitary spaces, quadratic forms in Euclidean and unitary spaces, finitedimensional space
Generalized functions by
I. M Gelʹfand(
Book
)
in English and held by 641 WorldCat member libraries worldwide
in English and held by 641 WorldCat member libraries worldwide
Elementary real and complex analysis by
G. E Shilov(
Book
)
21 editions published between 1973 and 2012 in English and held by 496 WorldCat member libraries worldwide
In this book the renowned Russian mathematician Georgi E. Shilov brings his unique perspective to real and complex analysis, an area of perennial interest in mathematics. Although there are many books available on the topic, the present work is specially designed for undergraduates in mathematics, science and engineering. A high level of mathematical sophistication is not required. The book begins with a systematic study of real numbers, understood to be a set of objects satisfying certain definite axioms. The concepts of a mathematical structure and an isomorphism are introduced in Chapter 2, after a brief digression on set theory, and a proof of the uniqueness of the structure of real numbers is given as an illustration. Two other structures are then introduced, namely ndimensional space and the field of complex numbers. After a detailed treatment of metric spaces in Chapter 3, a general theory of limits is developed in Chapter 4. Chapter 5 treats some theorems on continuous numerical functions on the real line, and then considers the use of functional equations to introduce the logarithm and the trigonometric functions. Chapter 6 is on infinite series, dealing not only with numerical series but also with series whose terms are vectors and functions (including power series). Chapters 7 and 8 treat differential calculus proper, with Taylor's series leading to a natural extension of real analysis into the complex domain. Chapter 9 presents the general theory of Riemann integration, together with a number of its applications. Analytic functions are covered in Chapter 10, while Chapter 11 is devoted to improper integrals, and makes full use of the technique of analytic functions. Each chapter includes a set of problems, with selected hints and answers at the end of the book. A wealth of examples and applications can be found throughout the text. Over 340 theorems are fully proved
21 editions published between 1973 and 2012 in English and held by 496 WorldCat member libraries worldwide
In this book the renowned Russian mathematician Georgi E. Shilov brings his unique perspective to real and complex analysis, an area of perennial interest in mathematics. Although there are many books available on the topic, the present work is specially designed for undergraduates in mathematics, science and engineering. A high level of mathematical sophistication is not required. The book begins with a systematic study of real numbers, understood to be a set of objects satisfying certain definite axioms. The concepts of a mathematical structure and an isomorphism are introduced in Chapter 2, after a brief digression on set theory, and a proof of the uniqueness of the structure of real numbers is given as an illustration. Two other structures are then introduced, namely ndimensional space and the field of complex numbers. After a detailed treatment of metric spaces in Chapter 3, a general theory of limits is developed in Chapter 4. Chapter 5 treats some theorems on continuous numerical functions on the real line, and then considers the use of functional equations to introduce the logarithm and the trigonometric functions. Chapter 6 is on infinite series, dealing not only with numerical series but also with series whose terms are vectors and functions (including power series). Chapters 7 and 8 treat differential calculus proper, with Taylor's series leading to a natural extension of real analysis into the complex domain. Chapter 9 presents the general theory of Riemann integration, together with a number of its applications. Analytic functions are covered in Chapter 10, while Chapter 11 is devoted to improper integrals, and makes full use of the technique of analytic functions. Each chapter includes a set of problems, with selected hints and answers at the end of the book. A wealth of examples and applications can be found throughout the text. Over 340 theorems are fully proved
Generalized functions and partial differential equations by
G. E Shilov(
Book
)
20 editions published in 1968 in English and held by 479 WorldCat member libraries worldwide
20 editions published in 1968 in English and held by 479 WorldCat member libraries worldwide
Mathematical analysis, a special course by
G. E Shilov(
Book
)
53 editions published between 1965 and 2016 in English and Undetermined and held by 440 WorldCat member libraries worldwide
Mathematical Analysis: A Special Course covers the fundamentals, principles, and theories that make up mathematical analysis
53 editions published between 1965 and 2016 in English and Undetermined and held by 440 WorldCat member libraries worldwide
Mathematical Analysis: A Special Course covers the fundamentals, principles, and theories that make up mathematical analysis
Elementary functional analysis by
G. E Shilov(
Book
)
20 editions published between 1974 and 2013 in English and Undetermined and held by 413 WorldCat member libraries worldwide
In this introductory work on mathematical analysis, the noted mathematician Georgi E. Shilov begins with an extensive and important chapter on the basic structures of mathematical analysis: linear spaces, metric spaces, normed linear spaces, Hilbert spaces, and normed algebras. The standard models for all these spaces are sets of functions (hence the term "functional analysis"), rather than sets of points in a finitedimensional space. Chapter 2 is devoted to differential equations, and contains the basic theorems on existence and uniqueness of solutions of ordinary differential equations for functions taking values in a Banach space. The solution of the linear equation with constant (operator) coefficients is written in general form in terms of the exponential of the operator. This leads, in the finitedimensional case, to explicit formulas not only for the solutions of firstorder equations, but also to the solutions of higherorder equations and systems of equations. The third chapter presents a theory of curvature for curve in a multidimensional space. The final two chapters essentially comprise an introduction to Fourier analysis. In the treatment of orthogonal expansions, a key role is played by Fourier series and the various kinds of convergence and summability for such series. The material on Fourier transforms, in addition to presenting the more familiar theory, also deals with problems in the complex domain, in particular with problems involving the Laplace transform. Designed for students at the upperundergraduate or graduate level, the text includes a set of problems for each chapter, with hints and answers at the end of the book
20 editions published between 1974 and 2013 in English and Undetermined and held by 413 WorldCat member libraries worldwide
In this introductory work on mathematical analysis, the noted mathematician Georgi E. Shilov begins with an extensive and important chapter on the basic structures of mathematical analysis: linear spaces, metric spaces, normed linear spaces, Hilbert spaces, and normed algebras. The standard models for all these spaces are sets of functions (hence the term "functional analysis"), rather than sets of points in a finitedimensional space. Chapter 2 is devoted to differential equations, and contains the basic theorems on existence and uniqueness of solutions of ordinary differential equations for functions taking values in a Banach space. The solution of the linear equation with constant (operator) coefficients is written in general form in terms of the exponential of the operator. This leads, in the finitedimensional case, to explicit formulas not only for the solutions of firstorder equations, but also to the solutions of higherorder equations and systems of equations. The third chapter presents a theory of curvature for curve in a multidimensional space. The final two chapters essentially comprise an introduction to Fourier analysis. In the treatment of orthogonal expansions, a key role is played by Fourier series and the various kinds of convergence and summability for such series. The material on Fourier transforms, in addition to presenting the more familiar theory, also deals with problems in the complex domain, in particular with problems involving the Laplace transform. Designed for students at the upperundergraduate or graduate level, the text includes a set of problems for each chapter, with hints and answers at the end of the book
How to construct graphs by
G. E Shilov(
Book
)
10 editions published in 1963 in English and held by 355 WorldCat member libraries worldwide
10 editions published in 1963 in English and held by 355 WorldCat member libraries worldwide
Verallgemeinerte Funktionen (Distributionen) by
I. M Gelʹfand(
Book
)
89 editions published between 1960 and 1969 in 3 languages and held by 318 WorldCat member libraries worldwide
Band 1
89 editions published between 1960 and 1969 in 3 languages and held by 318 WorldCat member libraries worldwide
Band 1
Commutative normed rings by
I. M Gelʹfand(
Book
)
36 editions published between 1957 and 2003 in 5 languages and held by 295 WorldCat member libraries worldwide
36 editions published between 1957 and 2003 in 5 languages and held by 295 WorldCat member libraries worldwide
Les distributions by
I. M Gelʹfand(
Book
)
25 editions published between 1962 and 1972 in French and English and held by 205 WorldCat member libraries worldwide
25 editions published between 1962 and 1972 in French and English and held by 205 WorldCat member libraries worldwide
Analyse mathématique Fonctions de plusieurs variables réelles by
G. E Shilov(
Book
)
34 editions published between 1973 and 1978 in 4 languages and held by 114 WorldCat member libraries worldwide
34 editions published between 1973 and 1978 in 4 languages and held by 114 WorldCat member libraries worldwide
Mathematical analysis by
G. E Shilov(
Book
)
6 editions published in 1973 in English and held by 102 WorldCat member libraries worldwide
6 editions published in 1973 in English and held by 102 WorldCat member libraries worldwide
Les distributions by
I. M Gelʹfand(
Book
)
15 editions published between 1962 and 1965 in French and English and held by 86 WorldCat member libraries worldwide
15 editions published between 1962 and 1965 in French and English and held by 86 WorldCat member libraries worldwide
Generalized Functions by
I. M Gelʹfand(
Book
)
22 editions published between 1964 and 2016 in English and Undetermined and held by 83 WorldCat member libraries worldwide
The first systematic theory of generalized functions (also known as distributions) was created in the early 1950s, although some aspects were developed much earlier, most notably in the definition of the Green's function in mathematics and in the work of Paul Dirac on quantum electrodynamics in physics. The sixvolume collection, Generalized Functions, written by I. M. Gel′fand and coauthors and published in Russian between 1958 and 1966, gives an introduction to generalized functions and presents various applications to analysis, PDE, stochastic processes, and representation theory. Volume 1
22 editions published between 1964 and 2016 in English and Undetermined and held by 83 WorldCat member libraries worldwide
The first systematic theory of generalized functions (also known as distributions) was created in the early 1950s, although some aspects were developed much earlier, most notably in the definition of the Green's function in mathematics and in the work of Paul Dirac on quantum electrodynamics in physics. The sixvolume collection, Generalized Functions, written by I. M. Gel′fand and coauthors and published in Russian between 1958 and 1966, gives an introduction to generalized functions and presents various applications to analysis, PDE, stochastic processes, and representation theory. Volume 1
Generalized functions by
I. M Gelʹfand(
Book
)
11 editions published between 1967 and 1982 in English and held by 66 WorldCat member libraries worldwide
The first systematic theory of generalized functions (also known as distributions) was created in the early 1950s, although some aspects were developed much earlier, most notably in the definition of the Green's function in mathematics and in the work of Paul Dirac on quantum electrodynamics in physics. The sixvolume collection, Generalized Functions, written by I. M. Gel′fand and coauthors and published in Russian between 1958 and 1966, gives an introduction to generalized functions and presents various applications to analysis, PDE, stochastic processes, and representation theory. In Volum
11 editions published between 1967 and 1982 in English and held by 66 WorldCat member libraries worldwide
The first systematic theory of generalized functions (also known as distributions) was created in the early 1950s, although some aspects were developed much earlier, most notably in the definition of the Green's function in mathematics and in the work of Paul Dirac on quantum electrodynamics in physics. The sixvolume collection, Generalized Functions, written by I. M. Gel′fand and coauthors and published in Russian between 1958 and 1966, gives an introduction to generalized functions and presents various applications to analysis, PDE, stochastic processes, and representation theory. In Volum
Analyse mathématique : fonctions d'une variable by
G. E Shilov(
Book
)
23 editions published between 1973 and 1978 in 3 languages and held by 65 WorldCat member libraries worldwide
23 editions published between 1973 and 1978 in 3 languages and held by 65 WorldCat member libraries worldwide
Theory of differential equations by
I. M Gelʹfand(
Book
)
16 editions published between 1967 and 2016 in 3 languages and held by 55 WorldCat member libraries worldwide
Theory of Differential Equations
16 editions published between 1967 and 2016 in 3 languages and held by 55 WorldCat member libraries worldwide
Theory of Differential Equations
Matematika v SSSR : 19581967 by
S. V Fomin(
Book
)
6 editions published between 1969 and 1970 in Russian and held by 13 WorldCat member libraries worldwide
6 editions published between 1969 and 1970 in Russian and held by 13 WorldCat member libraries worldwide
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Related Identities
 Gelʹfand, I. M. (Izrailʹ Moiseevich) Author Creator
 Silverman, Richard A. Other Translator Editor
 Gurevich, B. L. (Boris Lazarevich)
 Raĭkov, D. A. (Dmitriĭ Abramovich) Author
 Vilenkin, Naum Âkovlevič (19201991) Author Contributor
 Rideau, Guy Translator
 Vasilach, Serge Translator
 Saletan, Eugene J. (Eugene Jerome) 1924 Translator
 Fomin, S. V. (Sergeĭ Vasilʹevich) Contributor Editor Creator
 Kharine, Vitali Other Translator
Useful Links
Associated Subjects
Algebra Algebraic fields Algebras, Linear Banach algebras Banach spaces Calculus Differential equations Differential equations, Partial Functional analysis Functions Functions of real variables Functions of several real variables Generalized spaces Graphic methods Integrals, Generalized Mathematical analysis Mathematics Maxima and minima Measure theory Power, Tyrone, Rings (Algebra) Shilov, G. E.(Georgiĭ Evgenʹevich) Theory of distributions (Functional analysis) Vector analysis Vector spaces
Alternative Names
Bosse, Ûrij.
Chilov, G.
Chilov, G. E.
Chilov, G. E. 19171975
Chilov, Georgi E. 19171975
Chilov, Georgi Eugen 19171975
Chilov, Georgij Evgen'evič 19171975
Chilov, Gueorgi Evguenievitc
Chilov Gueorgi Evguenievitch
Georgi Jewgenjewitsch Schilow russischer Mathematiker
Georgij Evgen'evič Šilov matematico sovietico
Georgiy Shilov matemático ruso
Georgiy Shilov mathématicien russe
Georgiy Shilov Russisch wiskundige (19171975)
Georgiy Shilov Soviet mathematician
Gieorgij Szyłow
Schilow G. E.
Schilow, G. E. 19171975
Schilow, Georgii E. 19171975
Shilov, G.
Shilov, G. 19171975
Shilov, G.E.
Shilov, G. E. 19171975
Shilov, G. E. (Georgiĭ Evgenʹevich)
Shilov, G. E. (Georgiĭ Evgenʹevich), 19171975
Shilov, G. Y. 19171975
Shilov, G.Ye
Shilov, G. Ye 19171975
Shilov Georgi E.
Shilov, Georgi E. 19171975
Shilov, Georgi Eugen 19171975
Shilov, Georgi Evgenʹevich 19171975
Shilov, Georgi Ye.
Shilov, Georgii E.
Shilov, Georgii E. 19171975
Shilov Georgiĭ Evgenʹevich
Shilov, Georgiĭ Evgenʹevich 19171975
Shilov, Georgij E.
Shilov, Georgij Evgen'evič 19171975
Shilov, Georgij Evgenʹevich 19171975
Shilow, Georgi Eugen 19171975
Šilov, G. E.
Šilov, G. E. 19171975
Šilov, Georgij Evgen'evič
Šilov, Georgij Evgenʹevič 19171975
Шилов, Г. Е
Шилов, Г. Е. (Георгий Евгеньевич)
Шилов, Георгий Евгениевич
Шилов, Георгий Евгениевич, 19171975
Шилов, Георгий Евгеньевич
Шилов Георгій Євгенович
جورجي شيلوف عالم رياضي روسي
ゲオルギー・シロフ
シーロフ
シーロフ, G. E.
シーロフ, Г. E.
シーロフ, グーレヴィチ
喬治.希洛夫
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