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Book Synopsis Spectral methods in infinite-dimensional analysis. 2 (1995) by : I︠U︡riĭ Makarovich Berezanskiĭ
Download or read book Spectral methods in infinite-dimensional analysis. 2 (1995) written by I︠U︡riĭ Makarovich Berezanskiĭ and published by Springer Science & Business Media. This book was released on 1995 with total page 448 pages. Available in PDF, EPUB and Kindle. Book excerpt:
The Russian edition of this book appeared 5 years ago. Since that time, many results have been improved upon and new approaches to the problems investigated in the book have appeared. But the greatest surprise for us was to discover that there exists a large group of mathematicians working in the area of the so-called White Noise Analysis which is closely connected with the essential part of our book, namely, with the theory of generalized functions of infinitely many variables. The first papers dealing with White Noise Analysis were written by T. Hida in Japan in 1975. Later, this analysis was devel oped intensively in Japan, Germany, U.S.A., Taipei, and in other places. The related problems of infinite-dimensional analysis have been studied in Kiev since 1967, and the theory of generalized functions of infinitely many variables has been in vestigated since 1973. However, due to the political system in the U.S.S.R., contact be tween Ukrainian and foreign mathematicians was impossible for a long period of time. This is why, to our great regret, only at the end of 1988 did one of the authors meet L. Streit who told him about the existence of White Noise Analysis. And it become clear that many results in these two theories coincide and that, in fact, there exists a single theory and not two distinct ones.
Book Synopsis Spectral Methods in Infinite-Dimensional Analysis by : Yu.M. Berezansky
Download or read book Spectral Methods in Infinite-Dimensional Analysis written by Yu.M. Berezansky and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 983 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Russian edition of this book appeared 5 years ago. Since that time, many results have been improved upon and new approaches to the problems investigated in the book have appeared. But the greatest surprise for us was to discover that there exists a large group of mathematicians working in the area of the so-called White Noise Analysis which is closely connected with the essential part of our book, namely, with the theory of generalized functions of infinitely many variables. The first papers dealing with White Noise Analysis were written by T. Hida in Japan in 1975. Later, this analysis was devel oped intensively in Japan, Germany, U.S.A., Taipei, and in other places. The related problems of infinite-dimensional analysis have been studied in Kiev since 1967, and the theory of generalized functions of infinitely many variables has been in vestigated since 1973. However, due to the political system in the U.S.S.R., contact be tween Ukrainian and foreign mathematicians was impossible for a long period of time. This is why, to our great regret, only at the end of 1988 did one of the authors meet L. Streit who told him about the existence of White Noise Analysis. And it become clear that many results in these two theories coincide and that, in fact, there exists a single theory and not two distinct ones.
Book Synopsis Spectral methods in infinite-dimensional analysis. 1 (1995) by : I︠U︡riĭ Makarovich Berezanskiĭ
Download or read book Spectral methods in infinite-dimensional analysis. 1 (1995) written by I︠U︡riĭ Makarovich Berezanskiĭ and published by Springer Science & Business Media. This book was released on 1994 with total page 600 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Recent Developments in Infinite-Dimensional Analysis and Quantum Probability is dedicated to Professor Takeyuki Hida on the occasion of his 70th birthday. The book is more than a collection of articles. In fact, in it the reader will find a consistent editorial work, devoted to attempting to obtain a unitary picture from the different contributions and to give a comprehensive account of important recent developments in contemporary white noise analysis and some of its applications. For this reason, not only the latest results, but also motivations, explanations and connections with previous work have been included. The wealth of applications, from number theory to signal processing, from optimal filtering to information theory, from the statistics of stationary flows to quantum cable equations, show the power of white noise analysis as a tool. Beyond these, the authors emphasize its connections with practically all branches of contemporary probability, including stochastic geometry, the structure theory of stationary Gaussian processes, Neumann boundary value problems, and large deviations.
Book Synopsis Recent Developments in Infinite-Dimensional Analysis and Quantum Probability by : Luigi Accardi
Download or read book Recent Developments in Infinite-Dimensional Analysis and Quantum Probability written by Luigi Accardi and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 455 pages. Available in PDF, EPUB and Kindle. Book excerpt: Recent Developments in Infinite-Dimensional Analysis and Quantum Probability is dedicated to Professor Takeyuki Hida on the occasion of his 70th birthday. The book is more than a collection of articles. In fact, in it the reader will find a consistent editorial work, devoted to attempting to obtain a unitary picture from the different contributions and to give a comprehensive account of important recent developments in contemporary white noise analysis and some of its applications. For this reason, not only the latest results, but also motivations, explanations and connections with previous work have been included. The wealth of applications, from number theory to signal processing, from optimal filtering to information theory, from the statistics of stationary flows to quantum cable equations, show the power of white noise analysis as a tool. Beyond these, the authors emphasize its connections with practically all branches of contemporary probability, including stochastic geometry, the structure theory of stationary Gaussian processes, Neumann boundary value problems, and large deviations.
This volume contains a collection of original papers, associated with the International Conference on Partial Differential Equations, held in Potsdam, July 29 to August 2, 1996. The conference has taken place every year on a high scientific level since 1991; this event is connected with the activities of the Max Planck Research Group for Partial Differential Equations at Potsdam. Outstanding researchers and specialists from Armenia, Belarus, Belgium, Bulgaria, Canada, China, France, Germany, Great Britain, India, Israel, Italy, Japan, Poland, Romania, Russia, Spain, Sweden, Switzerland, Ukraine, and the USA contribute to this volume. The main topics concern recent progress in partial differential equations, microlocal analysis, pseudo-differential operators on manifolds with singularities, aspects in differential geometry and index theory, operator theory and operator algebras, stochastic spectral analysis, semigroups, Dirichlet forms, Schrodinger operators, semiclassical analysis, and scattering theory.
Book Synopsis Differential Equations, Asymptotic Analysis, and Mathematical Physics by : Michael Demuth
Download or read book Differential Equations, Asymptotic Analysis, and Mathematical Physics written by Michael Demuth and published by John Wiley & Sons. This book was released on 1997 with total page 436 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains a collection of original papers, associated with the International Conference on Partial Differential Equations, held in Potsdam, July 29 to August 2, 1996. The conference has taken place every year on a high scientific level since 1991; this event is connected with the activities of the Max Planck Research Group for Partial Differential Equations at Potsdam. Outstanding researchers and specialists from Armenia, Belarus, Belgium, Bulgaria, Canada, China, France, Germany, Great Britain, India, Israel, Italy, Japan, Poland, Romania, Russia, Spain, Sweden, Switzerland, Ukraine, and the USA contribute to this volume. The main topics concern recent progress in partial differential equations, microlocal analysis, pseudo-differential operators on manifolds with singularities, aspects in differential geometry and index theory, operator theory and operator algebras, stochastic spectral analysis, semigroups, Dirichlet forms, Schrodinger operators, semiclassical analysis, and scattering theory.
This volume presents a collection of papers covering applications from a wide range of systems with infinitely many degrees of freedom studied using techniques from stochastic and infinite dimensional analysis, e.g. Feynman path integrals, the statistical mechanics of polymer chains, complex networks, and quantum field theory. Systems of infinitely many degrees of freedom create their particular mathematical challenges which have been addressed by different mathematical theories, namely in the theories of stochastic processes, Malliavin calculus, and especially white noise analysis. These proceedings are inspired by a conference held on the occasion of Prof. Ludwig Streit’s 75th birthday and celebrate his pioneering and ongoing work in these fields.
Book Synopsis Stochastic and Infinite Dimensional Analysis by : Christopher C. Bernido
Download or read book Stochastic and Infinite Dimensional Analysis written by Christopher C. Bernido and published by Birkhäuser. This book was released on 2016-08-10 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents a collection of papers covering applications from a wide range of systems with infinitely many degrees of freedom studied using techniques from stochastic and infinite dimensional analysis, e.g. Feynman path integrals, the statistical mechanics of polymer chains, complex networks, and quantum field theory. Systems of infinitely many degrees of freedom create their particular mathematical challenges which have been addressed by different mathematical theories, namely in the theories of stochastic processes, Malliavin calculus, and especially white noise analysis. These proceedings are inspired by a conference held on the occasion of Prof. Ludwig Streit’s 75th birthday and celebrate his pioneering and ongoing work in these fields.
The book consists of articles based on the XXXVIII Białowieża Workshop on Geometric Methods in Physics, 2019. The series of Białowieża workshops, attended by a community of experts at the crossroads of mathematics and physics, is a major annual event in the field. The works in this book, based on presentations given at the workshop, are previously unpublished, at the cutting edge of current research, typically grounded in geometry and analysis, with applications to classical and quantum physics. For the past eight years, the Białowieża Workshops have been complemented by a School on Geometry and Physics, comprising series of advanced lectures for graduate students and early-career researchers. The extended abstracts of the five lecture series that were given in the eighth school are included. The unique character of the Workshop-and-School series draws on the venue, a famous historical, cultural and environmental site in the Białowieża forest, a UNESCO World Heritage Centre in the east of Poland: lectures are given in the Nature and Forest Museum and local traditions are interwoven with the scientific activities. The chapter “Toeplitz Extensions in Noncommutative Topology and Mathematical Physics” is available open access under a Creative Commons Attribution 4.0 International License via link.springer.com.
Book Synopsis Geometric Methods in Physics XXXVIII by : Piotr Kielanowski
Download or read book Geometric Methods in Physics XXXVIII written by Piotr Kielanowski and published by Springer Nature. This book was released on 2020-10-27 with total page 373 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book consists of articles based on the XXXVIII Białowieża Workshop on Geometric Methods in Physics, 2019. The series of Białowieża workshops, attended by a community of experts at the crossroads of mathematics and physics, is a major annual event in the field. The works in this book, based on presentations given at the workshop, are previously unpublished, at the cutting edge of current research, typically grounded in geometry and analysis, with applications to classical and quantum physics. For the past eight years, the Białowieża Workshops have been complemented by a School on Geometry and Physics, comprising series of advanced lectures for graduate students and early-career researchers. The extended abstracts of the five lecture series that were given in the eighth school are included. The unique character of the Workshop-and-School series draws on the venue, a famous historical, cultural and environmental site in the Białowieża forest, a UNESCO World Heritage Centre in the east of Poland: lectures are given in the Nature and Forest Museum and local traditions are interwoven with the scientific activities. The chapter “Toeplitz Extensions in Noncommutative Topology and Mathematical Physics” is available open access under a Creative Commons Attribution 4.0 International License via link.springer.com.
The infinite dimensional analysis as a branch of mathematical sciences was formed in the late 19th and early 20th centuries. Motivated by problems in mathematical physics, the first steps in this field were taken by V. Volterra, R. GateallX, P. Levy and M. Frechet, among others (see the preface to Levy[2]). Nevertheless, the most fruitful direction in this field is the infinite dimensional integration theory initiated by N. Wiener and A. N. Kolmogorov which is closely related to the developments of the theory of stochastic processes. It was Wiener who constructed for the first time in 1923 a probability measure on the space of all continuous functions (i. e. the Wiener measure) which provided an ideal math ematical model for Brownian motion. Then some important properties of Wiener integrals, especially the quasi-invariance of Gaussian measures, were discovered by R. Cameron and W. Martin[l, 2, 3]. In 1931, Kolmogorov[l] deduced a second partial differential equation for transition probabilities of Markov processes order with continuous trajectories (i. e. diffusion processes) and thus revealed the deep connection between theories of differential equations and stochastic processes. The stochastic analysis created by K. Ito (also independently by Gihman [1]) in the forties is essentially an infinitesimal analysis for trajectories of stochastic processes. By virtue of Ito's stochastic differential equations one can construct diffusion processes via direct probabilistic methods and treat them as function als of Brownian paths (i. e. the Wiener functionals).
Book Synopsis Introduction to Infinite Dimensional Stochastic Analysis by : Zhi-yuan Huang
Download or read book Introduction to Infinite Dimensional Stochastic Analysis written by Zhi-yuan Huang and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: The infinite dimensional analysis as a branch of mathematical sciences was formed in the late 19th and early 20th centuries. Motivated by problems in mathematical physics, the first steps in this field were taken by V. Volterra, R. GateallX, P. Levy and M. Frechet, among others (see the preface to Levy[2]). Nevertheless, the most fruitful direction in this field is the infinite dimensional integration theory initiated by N. Wiener and A. N. Kolmogorov which is closely related to the developments of the theory of stochastic processes. It was Wiener who constructed for the first time in 1923 a probability measure on the space of all continuous functions (i. e. the Wiener measure) which provided an ideal math ematical model for Brownian motion. Then some important properties of Wiener integrals, especially the quasi-invariance of Gaussian measures, were discovered by R. Cameron and W. Martin[l, 2, 3]. In 1931, Kolmogorov[l] deduced a second partial differential equation for transition probabilities of Markov processes order with continuous trajectories (i. e. diffusion processes) and thus revealed the deep connection between theories of differential equations and stochastic processes. The stochastic analysis created by K. Ito (also independently by Gihman [1]) in the forties is essentially an infinitesimal analysis for trajectories of stochastic processes. By virtue of Ito's stochastic differential equations one can construct diffusion processes via direct probabilistic methods and treat them as function als of Brownian paths (i. e. the Wiener functionals).
Together with the papers on the abstract operator theory are many papers on the theory of differential operators, boundary value problems, inverse scattering and other inverse problems, and on applications to biology, chemistry, wave propagation, and many other areas."--BOOK JACKET.
Book Synopsis Operator Theory and Its Applications by : Alexander G. Ramm
Download or read book Operator Theory and Its Applications written by Alexander G. Ramm and published by American Mathematical Soc.. This book was released on 2000 with total page 594 pages. Available in PDF, EPUB and Kindle. Book excerpt: Together with the papers on the abstract operator theory are many papers on the theory of differential operators, boundary value problems, inverse scattering and other inverse problems, and on applications to biology, chemistry, wave propagation, and many other areas."--BOOK JACKET.
This book collects original peer-reviewed contributions presented at the "International Conference on Mathematical Analysis and Applications (MAA 2020)" organized by the Department of Mathematics, National Institute of Technology Jamshedpur, India, from 2–4 November 2020. This book presents peer-reviewed research and survey papers in mathematical analysis that cover a broad range of areas including approximation theory, operator theory, fixed-point theory, function spaces, complex analysis, geometric and univalent function theory, control theory, fractional calculus, special functions, operation research, theory of inequalities, equilibrium problem, Fourier and wavelet analysis, mathematical physics, graph theory, stochastic orders and numerical analysis. Some chapters of the book discuss the applications to real-life situations. This book will be of value to researchers and students associated with the field of pure and applied mathematics.
Book Synopsis Mathematical Analysis and Applications by : Ouayl Chadli
Download or read book Mathematical Analysis and Applications written by Ouayl Chadli and published by Springer Nature. This book was released on 2022-03-22 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book collects original peer-reviewed contributions presented at the "International Conference on Mathematical Analysis and Applications (MAA 2020)" organized by the Department of Mathematics, National Institute of Technology Jamshedpur, India, from 2–4 November 2020. This book presents peer-reviewed research and survey papers in mathematical analysis that cover a broad range of areas including approximation theory, operator theory, fixed-point theory, function spaces, complex analysis, geometric and univalent function theory, control theory, fractional calculus, special functions, operation research, theory of inequalities, equilibrium problem, Fourier and wavelet analysis, mathematical physics, graph theory, stochastic orders and numerical analysis. Some chapters of the book discuss the applications to real-life situations. This book will be of value to researchers and students associated with the field of pure and applied mathematics.
