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  • Toeplitz Operators and Random Matrices

    In Memory of Harold Widom

    Series series Mathematics and Statistics (R0)
    This volume is dedicated to the memory of Harold Widom (1932–2021), an outstanding mathematician who has enriched mathematics with his ideas and ground breaking work since the 1950s until the present time.It contains a biography of Harold Widom, personal notes written by his former students or colleagues, and also his last, previously unpublished paper on domain walls in a Heisenberg–Ising chain. ... Read more

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  • Probability on Real Lie Algebras

    Series Book 206 - Cambridge Tracts in Mathematics
    This monograph is a progressive introduction to non-commutativity in probability theory, summarizing and synthesizing recent results about classical and quantum stochastic processes on Lie algebras. In the early chapters, focus is placed on concrete examples of the links between algebraic relations and the moments of probability distributions. The subsequent chapters are more advanced and deal ... Read more

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  • Differential Equations: An Introduction To Basic Concepts, Results And Applications (Third Edition)

    by Ioan I Vrabie ...
    This book presents, in a unitary frame and from a new perspective, the main concepts and results of one of the most fascinating branches of modern mathematics, namely differential equations, and offers the reader another point of view concerning a possible way to approach the problems of existence, uniqueness, approximation, and continuation of the solutions to a Cauchy problem. In addition, it ... Read more

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  • Hangzhou Lectures on Eigenfunctions of the Laplacian

    Series Book 188 - Annals of Mathematics Studies
    Based on lectures given at Zhejiang University in Hangzhou, China, and Johns Hopkins University, this book introduces eigenfunctions on Riemannian manifolds. Christopher Sogge gives a proof of the sharp Weyl formula for the distribution of eigenvalues of Laplace-Beltrami operators, as well as an improved version of the Weyl formula, the Duistermaat-Guillemin theorem under natural assumptions on ... Read more

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  • Mathematics Without Boundaries

    Surveys in Pure Mathematics

    Series series Mathematics and Statistics (R0)
    The contributions in this volume have been written by eminent scientists from the international mathematical community and present significant advances in several theories, methods and problems of Mathematical Analysis, Discrete Mathematics, Geometry and their Applications. The chapters focus on both old and recent developments in Functional Analysis, Harmonic Analysis, Complex Analysis, Operator ... Read more

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  • Stochastic Partial Differential Equations

    Series series Mathematics and Statistics (R0)
    Taking readers with a basic knowledge of probability and real analysis to the frontiers of a very active research discipline, this textbook provides all the necessary background from functional analysis and the theory of PDEs. It covers the main types of equations (elliptic, hyperbolic and parabolic) and discusses different types of random forcing. The objective is to give the reader the necessary ... Read more

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  • Handbook of Differential Equations: Stationary Partial Differential Equations

    Edited by Michel Chipot ...
    Series Book 6 - Handbook of Differential Equations: Stationary Partial Differential Equations
    This handbook is the sixth and last volume in the series devoted to stationary partial differential equations. The topics covered by this volume include in particular domain perturbations for boundary value problems, singular solutions of semilinear elliptic problems, positive solutions to elliptic equations on unbounded domains, symmetry of solutions, stationary compressible Navier-Stokes ... Read more

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  • Brownian Motion

    Series Book 30 - Cambridge Series in Statistical and Probabilistic Mathematics
    This eagerly awaited textbook covers everything the graduate student in probability wants to know about Brownian motion, as well as the latest research in the area. Starting with the construction of Brownian motion, the book then proceeds to sample path properties like continuity and nowhere differentiability. Notions of fractal dimension are introduced early and are used throughout the book to ... Read more

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  • Exercises And Problems In Linear Algebra

    by John M Erdman ...
    This book contains an extensive collection of exercises and problems that address relevant topics in linear algebra. Topics that the author finds missing or inadequately covered in most existing books are also included. The exercises will be both interesting and helpful to an average student. Some are fairly routine calculations, while others require serious thought.The format of the questions ... Read more

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  • Introduction to Matrix Analysis and Applications

    Series series Mathematics and Statistics (R0)
    Matrices can be studied in different ways. They are a linear algebraic structure and have a topological/analytical aspect (for example, the normed space of matrices) and they also carry an order structure that is induced by positive semidefinite matrices. The interplay of these closely related structures is an essential feature of matrix analysis.This book explains these aspects of matrix analysis ... Read more

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  • Highlights in Lie Algebraic Methods

    Series series Mathematics and Statistics (R0)
    This volume consists of expository and research articles that highlight the various Lie algebraic methods used in mathematical research today. Key topics discussed include spherical varieties, Littelmann Paths and Kac–Moody Lie algebras, modular representations, primitive ideals, representation theory of Artin algebras and quivers, Kac–Moody superalgebras, categories of Harish–Chandra modules, ... Read more

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  • Nonlinearity and Functional Analysis

    Lectures on Nonlinear Problems in Mathematical Analysis

    Nonlinearity and Functional Analysis is a collection of lectures that aim to present a systematic description of fundamental nonlinear results and their applicability to a variety of concrete problems taken from various fields of mathematical analysis. For decades, great mathematical interest has focused on problems associated with linear operators and the extension of the well-known results of ... Read more

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