Laugesen, Richard 1967
Overview
Works:  17 works in 23 publications in 1 language and 183 library holdings 

Genres:  Academic theses 
Roles:  Other 
Classifications:  QA10.5, 510.23 
Publication Timeline
.
Most widely held works by
Richard Laugesen
Symmetrization in analysis by
Albert Baernstein(
)
2 editions published in 2019 in English and held by 94 WorldCat member libraries worldwide
Symmetrization is a rich area of mathematical analysis whose history reaches back to antiquity. This book presents many aspects of the theory, including symmetric decreasing rearrangement and circular and Steiner symmetrization in Euclidean spaces, spheres and hyperbolic spaces. Many energies, frequencies, capacities, eigenvalues, perimeters and function norms are shown to either decrease or increase under symmetrization. The book begins by focusing on Euclidean space, building up from twopoint polarization with respect to hyperplanes. Background material in geometric measure theory and analysis is carefully developed, yielding selfcontained proofs of all the major theorems. This leads to the analysis of functions defined on spheres and hyperbolic spaces, and then to convolutions, multiple integrals and hypercontractivity of the Poisson semigroup. The author's 'star function' method, which preserves subharmonicity, is developed with applications to semilinear PDEs. The book concludes with a thorough selfcontained account of the star function's role in complex analysis, covering value distribution theory, conformal mapping and the hyperbolic metric
2 editions published in 2019 in English and held by 94 WorldCat member libraries worldwide
Symmetrization is a rich area of mathematical analysis whose history reaches back to antiquity. This book presents many aspects of the theory, including symmetric decreasing rearrangement and circular and Steiner symmetrization in Euclidean spaces, spheres and hyperbolic spaces. Many energies, frequencies, capacities, eigenvalues, perimeters and function norms are shown to either decrease or increase under symmetrization. The book begins by focusing on Euclidean space, building up from twopoint polarization with respect to hyperplanes. Background material in geometric measure theory and analysis is carefully developed, yielding selfcontained proofs of all the major theorems. This leads to the analysis of functions defined on spheres and hyperbolic spaces, and then to convolutions, multiple integrals and hypercontractivity of the Poisson semigroup. The author's 'star function' method, which preserves subharmonicity, is developed with applications to semilinear PDEs. The book concludes with a thorough selfcontained account of the star function's role in complex analysis, covering value distribution theory, conformal mapping and the hyperbolic metric
BIG jobs guide : business, industry, and government careers for mathematical scientists, statisticians, and operations researchers by
Rachel Levy(
Book
)
5 editions published in 2018 in English and held by 62 WorldCat member libraries worldwide
"Jobs using mathematics, statistics, and operations research are projected to grow by almost 30% over the next decade. BIG Jobs Guide helps job seekers at every stage of their careers in these fields explore opportunities in business, industry, and government (BIG). Written in a conversational and practical tone, BIG Jobs Guide offers insight on topics such as: What skills can I offer employers? How do I write a highimpact resume? Where can I find a rewarding internship? What kinds of jobs are out there for me? The Guide also offers insights to advisors and mentors on topics such as how departments can help students get BIG jobs and how faculty members and internship mentors can build institutional relationships. Whether you're an undergraduate or graduate student or a job seeker in applied mathematics, statistics, computer science, or operations research, this handson book will help you reach your goal, whether landing an internship, getting your first job or transitioning to a new one."Amazon.com
5 editions published in 2018 in English and held by 62 WorldCat member libraries worldwide
"Jobs using mathematics, statistics, and operations research are projected to grow by almost 30% over the next decade. BIG Jobs Guide helps job seekers at every stage of their careers in these fields explore opportunities in business, industry, and government (BIG). Written in a conversational and practical tone, BIG Jobs Guide offers insight on topics such as: What skills can I offer employers? How do I write a highimpact resume? Where can I find a rewarding internship? What kinds of jobs are out there for me? The Guide also offers insights to advisors and mentors on topics such as how departments can help students get BIG jobs and how faculty members and internship mentors can build institutional relationships. Whether you're an undergraduate or graduate student or a job seeker in applied mathematics, statistics, computer science, or operations research, this handson book will help you reach your goal, whether landing an internship, getting your first job or transitioning to a new one."Amazon.com
Symmetrization in analysis by
Albert Baernstein(
)
1 edition published in 2019 in English and held by 5 WorldCat member libraries worldwide
1 edition published in 2019 in English and held by 5 WorldCat member libraries worldwide
Approximation and spanning in the Hardy space, by affine systems by
HuyQui Bui(
Book
)
1 edition published in 2005 in English and held by 3 WorldCat member libraries worldwide
1 edition published in 2005 in English and held by 3 WorldCat member libraries worldwide
Spanning and sampling in Lebesgue and Sobolev spaces by
HuyQui Bui(
Book
)
1 edition published in 2004 in English and held by 3 WorldCat member libraries worldwide
1 edition published in 2004 in English and held by 3 WorldCat member libraries worldwide
Developing specialist language styles : research & application by
Mitch O'Toole(
Book
)
1 edition published in 2011 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 2011 in English and held by 2 WorldCat member libraries worldwide
Gabor frames with trigonometric spline dual windows by Inmi Kim(
)
1 edition published in 2011 in English and held by 2 WorldCat member libraries worldwide
A Gabor system is a collection of modulated and translated copies of a window function. If we have a signal in $L^2(mathbb{R})$, it can be analyzed with a Gabor system generated by a certain window $g$ and then synthesized with a Gabor system generated by another window $h$. If this leads us to a perfect reconstruction, we say that $g$ and $h$ are dual Gabor windows. Few explicit examples of dual window pairs are known. This thesis constructs explicit examples of Gabor dual windows with trigonometric form. The windows have fixed support and have an arbitrary smoothness. Also, in the discrete time domain, the trigonometric form allows us to evaluate the Gabor coefficients efficiently using the Discrete Fourier Transform. For the higher dimensional cases, we find window examples for a large class of modulation parameter lattices, including shear lattices. Also, a sufficient condition on the norm of the modulation lattice to have explicit dual Gabor windows is presented, for every dimension
1 edition published in 2011 in English and held by 2 WorldCat member libraries worldwide
A Gabor system is a collection of modulated and translated copies of a window function. If we have a signal in $L^2(mathbb{R})$, it can be analyzed with a Gabor system generated by a certain window $g$ and then synthesized with a Gabor system generated by another window $h$. If this leads us to a perfect reconstruction, we say that $g$ and $h$ are dual Gabor windows. Few explicit examples of dual window pairs are known. This thesis constructs explicit examples of Gabor dual windows with trigonometric form. The windows have fixed support and have an arbitrary smoothness. Also, in the discrete time domain, the trigonometric form allows us to evaluate the Gabor coefficients efficiently using the Discrete Fourier Transform. For the higher dimensional cases, we find window examples for a large class of modulation parameter lattices, including shear lattices. Also, a sufficient condition on the norm of the modulation lattice to have explicit dual Gabor windows is presented, for every dimension
Dispersive estimates for the Schrdinger equation by William R Green(
)
1 edition published in 2010 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 2010 in English and held by 2 WorldCat member libraries worldwide
Sobolev spaces and approximation by affine spanning systems by
HuyQui Bui(
Book
)
1 edition published in 2006 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 2006 in English and held by 2 WorldCat member libraries worldwide
Dynamical systems on networks by
Timothy Ferguson(
)
1 edition published in 2018 in English and held by 1 WorldCat member library worldwide
We obtain results for two distinct dynamical models: the Kuramoto model, a general model for coupled oscillator systems, and a model for opinion formation in social networks. Our main focus is on understanding the fixed points of these systems and their stability. For many models the stability of such fixed points can be studied with a Laplacian matrix. We give a formula for the inertia of these matrices, characterizing the real parts of the spectrum, by relating them to another matrix depending on the network topology. We then study the Kuramoto model, and in particular, the phenomena of synchronization, when all oscillators rotate at a common frequency, which corresponds to a fixed point. This phenomenon is wellknown to depend on the natural frequencies of the oscillators and, more specifically, that the chance of synchronization increases if the natural frequencies are more similar. We then give upper and lower bounds for the volume of the set such frequencies in frequency space. Our bounds can be formulated in terms of sums over spanning trees which we further use to deduce that the volume is intimately related to the number of spanning trees for dense networks. We also characterize the structure of fixed points of the Kuramoto model by showing that every fixed point corresponds to a lattice point in a certain set which records how the phaseangles wrap around cycles in the network. As a consequence, under mild conditions, we derive the rate of growth of the number of fixed points as we consider increasingly large graphs with fixed topology. We also consider a model for opinion formation in social networks. More specifically, we characterize the global minima of an energy functional, intuitively the ``most stable" configurations, when the network is ``balanced" as well as show that the number of stable configurations can increase as we increase the strengths of the relationships in the network. Finally, we describe an algorithm for generating certain random networks. These networks are generalizations of Erd\H{o}sR\'{e}nyi graphs with correlations between pairs of edges depending on the particular pattern they create. We then use this algorithm to study the effect on fixed points of network properties and therefore the dynamics of the Kuramoto model
1 edition published in 2018 in English and held by 1 WorldCat member library worldwide
We obtain results for two distinct dynamical models: the Kuramoto model, a general model for coupled oscillator systems, and a model for opinion formation in social networks. Our main focus is on understanding the fixed points of these systems and their stability. For many models the stability of such fixed points can be studied with a Laplacian matrix. We give a formula for the inertia of these matrices, characterizing the real parts of the spectrum, by relating them to another matrix depending on the network topology. We then study the Kuramoto model, and in particular, the phenomena of synchronization, when all oscillators rotate at a common frequency, which corresponds to a fixed point. This phenomenon is wellknown to depend on the natural frequencies of the oscillators and, more specifically, that the chance of synchronization increases if the natural frequencies are more similar. We then give upper and lower bounds for the volume of the set such frequencies in frequency space. Our bounds can be formulated in terms of sums over spanning trees which we further use to deduce that the volume is intimately related to the number of spanning trees for dense networks. We also characterize the structure of fixed points of the Kuramoto model by showing that every fixed point corresponds to a lattice point in a certain set which records how the phaseangles wrap around cycles in the network. As a consequence, under mild conditions, we derive the rate of growth of the number of fixed points as we consider increasingly large graphs with fixed topology. We also consider a model for opinion formation in social networks. More specifically, we characterize the global minima of an energy functional, intuitively the ``most stable" configurations, when the network is ``balanced" as well as show that the number of stable configurations can increase as we increase the strengths of the relationships in the network. Finally, we describe an algorithm for generating certain random networks. These networks are generalizations of Erd\H{o}sR\'{e}nyi graphs with correlations between pairs of edges depending on the particular pattern they create. We then use this algorithm to study the effect on fixed points of network properties and therefore the dynamics of the Kuramoto model
Linear and bilinear restriction estimates for the Fourier transform by Faruk Temur(
)
2 editions published in 2013 in English and held by 1 WorldCat member library worldwide
2 editions published in 2013 in English and held by 1 WorldCat member library worldwide
A new computation of the Bergman kernel and related techniques by Zhenghui Huo(
)
1 edition published in 2016 in English and held by 1 WorldCat member library worldwide
We introduce a technique for obtaining the Bergman kernel on certain Hartogs domains. To do so, we apply a differential operator to a known kernel function on a domain in lower dimensional space. We rediscover some known results and we obtain new explicit formulas. Using these formulas, we analyze the boundary behavior of the kernel function on the diagonal. Our technique also leads us to results about a cancellation of singularities for generalized hypergeometric functions and weighted Bergman kernels. Finally, we give an alternative approach to obtain explicit bases for complex harmonic homogeneous polynomial spaces
1 edition published in 2016 in English and held by 1 WorldCat member library worldwide
We introduce a technique for obtaining the Bergman kernel on certain Hartogs domains. To do so, we apply a differential operator to a known kernel function on a domain in lower dimensional space. We rediscover some known results and we obtain new explicit formulas. Using these formulas, we analyze the boundary behavior of the kernel function on the diagonal. Our technique also leads us to results about a cancellation of singularities for generalized hypergeometric functions and weighted Bergman kernels. Finally, we give an alternative approach to obtain explicit bases for complex harmonic homogeneous polynomial spaces
A sharp Schr©œdinger maximal estimate in R2 by Xiumin Du(
)
1 edition published in 2017 in English and held by 1 WorldCat member library worldwide
We study the almost everywhere pointwise convergence of the solutions to Schr©œdinger equations in $\mathbb{R}^2$. It is shown that $\lim_{t \to 0} e^{it\Delta}f(x) = f(x)$ almost everywhere for all $f \in H^s (\mathbb{R}^2)$ provided that $s>1/3$. This result is sharp up to the endpoint. It comes from the following Schr©œdinger maximal estimate: $$ \left\ \sup_{0 <t \leq 1}  e^{it \Delta} f \right\_{L^3(B(0,1))} \leq C_s \ f \_{H^s(\mathbb{R}^2)}\, $$ for any $s> 1/3$ and any function $f \in H^s(\mathbb{R}^2)$. The proof uses polynomial partitioning and decoupling
1 edition published in 2017 in English and held by 1 WorldCat member library worldwide
We study the almost everywhere pointwise convergence of the solutions to Schr©œdinger equations in $\mathbb{R}^2$. It is shown that $\lim_{t \to 0} e^{it\Delta}f(x) = f(x)$ almost everywhere for all $f \in H^s (\mathbb{R}^2)$ provided that $s>1/3$. This result is sharp up to the endpoint. It comes from the following Schr©œdinger maximal estimate: $$ \left\ \sup_{0 <t \leq 1}  e^{it \Delta} f \right\_{L^3(B(0,1))} \leq C_s \ f \_{H^s(\mathbb{R}^2)}\, $$ for any $s> 1/3$ and any function $f \in H^s(\mathbb{R}^2)$. The proof uses polynomial partitioning and decoupling
Modulational instability in some shallow water wave models by Ashish Kumar Pandey(
)
1 edition published in 2018 in English and held by 1 WorldCat member library worldwide
Modulational or BenjaminFeir instability is a well known phenomenon of Stokes' periodic waves on the water surface. In this dissertation, we study this phenomenon for periodic traveling wave solutions of various shallow water wave models. We study the spectral stability or instability with respect to long wave length perturbations of small amplitude periodic traveling waves of shallow water wave models like BenjaminBonaMahony and CamassaHolm equations. We propose a bidirectional shallow water model which generalizes Whitham equation to contain the nonlinearities of nonlinear shallow water equations. The analysis yields a modulational instability index for each model which is solely determined by the wavenumber of underlying periodic traveling wave. For a fixed wavenumber, the sign of the index determines modulational instability. We also includes the effects of surface tension in fulldispersion shallow water models and study its effects on modulational instability
1 edition published in 2018 in English and held by 1 WorldCat member library worldwide
Modulational or BenjaminFeir instability is a well known phenomenon of Stokes' periodic waves on the water surface. In this dissertation, we study this phenomenon for periodic traveling wave solutions of various shallow water wave models. We study the spectral stability or instability with respect to long wave length perturbations of small amplitude periodic traveling waves of shallow water wave models like BenjaminBonaMahony and CamassaHolm equations. We propose a bidirectional shallow water model which generalizes Whitham equation to contain the nonlinearities of nonlinear shallow water equations. The analysis yields a modulational instability index for each model which is solely determined by the wavenumber of underlying periodic traveling wave. For a fixed wavenumber, the sign of the index determines modulational instability. We also includes the effects of surface tension in fulldispersion shallow water models and study its effects on modulational instability
Spectral problems on triangles and disks: Extremizers and ground states by Sarah Son(
)
1 edition published in 2014 in English and held by 1 WorldCat member library worldwide
1 edition published in 2014 in English and held by 1 WorldCat member library worldwide
SturmLiouville estimates for the spectrum and Cheeger constant by
Brian Benson(
)
1 edition published in 2014 in English and held by 1 WorldCat member library worldwide
1 edition published in 2014 in English and held by 1 WorldCat member library worldwide
Asymptotic stability and completeness in 2D nonlinear schrodinger equation by Ruth Skulkhu(
)
1 edition published in 2012 in English and held by 1 WorldCat member library worldwide
1 edition published in 2012 in English and held by 1 WorldCat member library worldwide
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Alternative Names
Laugesen, R. S. 1967
Laugesen, Richard 1967
Laugesen, Richard Snyder 1967
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