Pseudodifferential Methods In Number Theory

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Pseudodifferential Methods In Number Theory

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Author : André Unterberger
language : en
Publisher: Birkhäuser
Release Date : 2018-07-16

Pseudodifferential Methods In Number Theory written by André Unterberger and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-07-16 with Mathematics categories.

Classically developed as a tool for partial differential equations, the analysis of operators known as pseudodifferential analysis is here regarded as a possible help in questions of arithmetic. The operators which make up the main subject of the book can be characterized in terms of congruence arithmetic. They enjoy a Eulerian structure, and are applied to the search for new conditions equivalent to the Riemann hypothesis. These consist in the validity of certain parameter-dependent estimates for a class of Hermitian forms of finite rank. The Littlewood criterion, involving sums of Möbius coefficients, and the Weil so-called explicit formula, which leads to his positivity criterion, fit within this scheme, using in the first case Weyl's pseudodifferential calculus, in the second case Fuchs'. The book should be of interest to people looking for new possible approaches to the Riemann hypothesis, also to new perspectives on pseudodifferential analysis and on the way it combines with modular form theory. Analysts will have no difficulty with the arithmetic aspects, with which, save for very few exceptions, no previous acquaintance is necessary.

Elementary Introduction To The Theory Of Pseudodifferential Operators

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Author : Xavier Saint Raymond
language : en
Publisher: CRC Press
Release Date : 1991-09-17

Elementary Introduction To The Theory Of Pseudodifferential Operators written by Xavier Saint Raymond and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991-09-17 with Mathematics categories.

In the 19th century, the Fourier transformation was introduced to study various problems of partial differential equations. Since 1960, this old tool has been developed into a well-organized theory called microlocal analysis that is based on the concept of the pseudo-differential operator. This book provides the fundamental knowledge non-specialists need in order to use microlocal analysis. It is strictly mathematical in the sense that it contains precise definitions, statements of theorems and complete proofs, and follows the usual method of pure mathematics. The book explains the origin of the theory (i.e., Fourier transformation), presents an elementary construcion of distribution theory, and features a careful exposition of standard pseudodifferential theory. Exercises, historical notes, and bibliographical references are included to round out this essential book for mathematics students; engineers, physicists, and mathematicians who use partial differential equations; and advanced mathematics instructors.

Distributions And Operators

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Author : Gerd Grubb
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-10-10

Distributions And Operators written by Gerd Grubb and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-10-10 with Mathematics categories.

This book gives an introduction to distribution theory, based on the work of Schwartz and of many other people. It is the first book to present distribution theory as a standard text. Each chapter has been enhanced with many exercises and examples.

Periodic Integral And Pseudodifferential Equations With Numerical Approximation

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Author : Jukka Saranen
language : en
Publisher: Springer Science & Business Media
Release Date : 2001-11-06

Periodic Integral And Pseudodifferential Equations With Numerical Approximation written by Jukka Saranen and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-11-06 with Mathematics categories.

An attractive book on the intersection of analysis and numerical analysis, deriving classical boundary integral equations arising from the potential theory and acoustics. This self-contained monograph can be used as a textbook by graduate/postgraduate students. It also contains a lot of carefully chosen exercises.

Analytic Methods In The Theory Of Differential And Pseudo Differential Equations Of Parabolic Type

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Author : Samuil D. Eidelman
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06

Analytic Methods In The Theory Of Differential And Pseudo Differential Equations Of Parabolic Type written by Samuil D. Eidelman and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

The theory of parabolic equations, a well-developed part of the contemporary partial differential equations and mathematical physics, is the subject theory of of an immense research activity. A continuing interest in parabolic equations is caused both by the depth and complexity of mathematical problems emerging here, and by its importance in specific applied problems of natural science, technology, and economics. This book aims at a consistent and, as far as possible, a complete exposition of analytic methods of constructing, investigating, and using fundamental solutions of the Cauchy problem for the following four classes of linear parabolic equations with coefficients depending on all variables: -7 E : 2b-parabolic partial differential equations (parabolic equations of a qua- l homogeneous structure), in which every spatial variable may have its own to the time variable. weight with respect E : degenerate partial differential equations of Kolmogorov's structure, which 2 generalize classical Kolmogorov equations of diffusion with inertia. E3: pseudo-differential equations with non-smooth quasi-homogeneous symbols. E : fractional diffusion equations. 4 These classes of equations generalize in various directions the classical equations and systems parabolic in the Petrovsky sense, which were defined in [180] and studied in a number of monographs [83, 45, 146, 107, 76] and survey articles [102, 1, 215, 70, 46].

Operator Algebras Toeplitz Operators And Related Topics

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Author : Wolfram Bauer
language : en
Publisher: Springer Nature
Release Date : 2020-09-01

Operator Algebras Toeplitz Operators And Related Topics written by Wolfram Bauer and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-09-01 with Mathematics categories.

This book features a collection of up-to-date research papers that study various aspects of general operator algebra theory and concrete classes of operators, including a range of applications. Most of the papers included were presented at the International Workshop on Operator Algebras, Toeplitz Operators, and Related Topics, in Boca del Rio, Veracruz, Mexico, in November 2018. The conference, which was attended by more than 30 leading experts in the field, was held in celebration of Nikolai Vasilevski’s 70th birthday, and the contributions are dedicated to him.

Pseudo Differential Operators

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Author : Hans G. Feichtinger
language : en
Publisher: Springer
Release Date : 2008-08-15

Pseudo Differential Operators written by Hans G. Feichtinger and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-08-15 with Mathematics categories.

Pseudo-differential operators were initiated by Kohn, Nirenberg and Hörmander in the sixties of the last century. Beside applications in the general theory of partial differential equations, they have their roots also in the study of quantization first envisaged by Hermann Weyl thirty years earlier. Thanks to the understanding of the connections of wavelets with other branches of mathematical analysis, quantum physics and engineering, such operators have been used under different names as mathematical models in signal analysis since the last decade of the last century. The volume investigates the mathematics of quantization and signals in the context of pseudo-differential operators, Weyl transforms, Daubechies operators, Wick quantization and time-frequency localization operators. Applications to quantization, signal analysis and the modern theory of PDE are highlighted.

International Conference On Analytic Methods In Number Theory And Analysis Moscow 14 19 September 1981

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Author :
language : en
Publisher: American Mathematical Soc.
Release Date : 1986

International Conference On Analytic Methods In Number Theory And Analysis Moscow 14 19 September 1981 written by and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986 with Mathematics categories.

This collection consists of papers delivered at an international conference by the most eminent specialists in the domains of number theory, algebra, and analysis. The papers are devoted to actual problems in these domains of mathematics. In addition, short communications presented by participants in the conference are included.

Pseudo Differential Operators Analysis Applications And Computations

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Author : Luigi Rodino
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-03-13

Pseudo Differential Operators Analysis Applications And Computations written by Luigi Rodino and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-03-13 with Mathematics categories.

This volume consists of eighteen peer-reviewed papers related to lectures on pseudo-differential operators presented at the meeting of the ISAAC Group in Pseudo-Differential Operators (IGPDO) held at Imperial College London on July 13-18, 2009. Featured in this volume are the analysis, applications and computations of pseudo-differential operators in mathematics, physics and signal analysis. This volume is a useful complement to the volumes “Advances in Pseudo-Differential Operators”, “Pseudo-Differential Operators and Related Topics”, “Modern Trends in Pseudo-Differential Operators”, “New Developments in Pseudo-Differential Operators” and “Pseudo-Differential Operators: Complex Analysis and Partial Differential Equations” published in the same series in, respectively, 2004, 2006, 2007, 2009 and 2010.

Pseudo Differential Operators Generalized Functions And Asymptotics

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Author : Shahla Molahajloo
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-02-26

Pseudo Differential Operators Generalized Functions And Asymptotics written by Shahla Molahajloo and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-02-26 with Mathematics categories.

This volume consists of twenty peer-reviewed papers from the special session on pseudodifferential operators and the special session on generalized functions and asymptotics at the Eighth Congress of ISAAC held at the Peoples’ Friendship University of Russia in Moscow on August 22‒27, 2011. The category of papers on pseudo-differential operators contains such topics as elliptic operators assigned to diffeomorphisms of smooth manifolds, analysis on singular manifolds with edges, heat kernels and Green functions of sub-Laplacians on the Heisenberg group and Lie groups with more complexities than but closely related to the Heisenberg group, Lp-boundedness of pseudo-differential operators on the torus, and pseudo-differential operators related to time-frequency analysis. The second group of papers contains various classes of distributions and algebras of generalized functions with applications in linear and nonlinear differential equations, initial value problems and boundary value problems, stochastic and Malliavin-type differential equations. This second group of papers are related to the third collection of papers via the setting of Colombeau-type spaces and algebras in which microlocal analysis is developed by means of techniques in asymptotics. The volume contains the synergies of the three areas treated and is a useful complement to volumes 155, 164, 172, 189, 205 and 213 published in the same series in, respectively, 2004, 2006, 2007, 2009, 2010 and 2011.