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Pseudodifferential Methods In Number Theory
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Book Synopsis Pseudodifferential Methods in Number Theory by : André Unterberger
Download or read book Pseudodifferential Methods in Number Theory written by André Unterberger and published by Birkhäuser. This book was released on 2018-07-16 with total page 173 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Elementary Introduction to the Theory of Pseudodifferential Operators by : Xavier Saint Raymond
Download or read book Elementary Introduction to the Theory of Pseudodifferential Operators written by Xavier Saint Raymond and published by Routledge. This book was released on 2018-02-06 with total page 71 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Functional Calculus of Pseudodifferential Boundary Problems by : Gerd Grubb
Download or read book Functional Calculus of Pseudodifferential Boundary Problems written by Gerd Grubb and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 536 pages. Available in PDF, EPUB and Kindle. Book excerpt: Pseudodifferential methods are central to the study of partial differential equations, because they permit an "algebraization." The main purpose of this book is to set up an operational calculus for operators defined from differential and pseudodifferential boundary values problems via a resolvent construction. A secondary purposed is to give a complete treatment of the properties of the calculus of pseudodifferential boundary problems with transmission, both the first version by Boutet de Monvel (brought completely up to date in this edition) and in version containing a parameter running in an unbounded set. And finally, the book presents some applications to evolution problems, index theory, fractional powers, spectral theory and singular perturbation theory. Thus the book’s improved proofs and modern points of view will be useful to research mathematicians and to graduate students studying partial differential equations and pseudodifferential operators.
Book Synopsis Analytic Methods In The Theory Of Differential And Pseudo-Differential Equations Of Parabolic Type by : Samuil D. Eidelman
Download or read book Analytic Methods In The Theory Of Differential And Pseudo-Differential Equations Of Parabolic Type written by Samuil D. Eidelman and published by Birkhäuser. This book was released on 2012-12-06 with total page 390 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to new classes of parabolic differential and pseudo-differential equations extensively studied in the last decades, such as parabolic systems of a quasi-homogeneous structure, degenerate equations of the Kolmogorov type, pseudo-differential parabolic equations, and fractional diffusion equations. It will appeal to mathematicians interested in new classes of partial differential equations, and physicists specializing in diffusion processes.
Book Synopsis Periodic Integral and Pseudodifferential Equations with Numerical Approximation by : Jukka Saranen
Download or read book Periodic Integral and Pseudodifferential Equations with Numerical Approximation written by Jukka Saranen and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 461 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Pseudodifferential Operators with Automorphic Symbols by : André Unterberger
Download or read book Pseudodifferential Operators with Automorphic Symbols written by André Unterberger and published by Birkhäuser. This book was released on 2015-06-22 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main results of this book combine pseudo differential analysis with modular form theory. The methods rely for the most part on explicit spectral theory and the extended use of special functions. The starting point is a notion of modular distribution in the plane, which will be new to most readers and relates under the Radon transformation to the classical one of modular form of the non-holomorphic type. Modular forms of the holomorphic type are addressed too in a more concise way, within a general scheme dealing with quantization theory and elementary, but novel, representation-theoretic concepts.
Book Synopsis Pseudodifferential Operators and Nonlinear PDE by : Michael Taylor
Download or read book Pseudodifferential Operators and Nonlinear PDE written by Michael Taylor and published by Springer Science & Business Media. This book was released on 1991-11-01 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt: For the past 25 years the theory of pseudodifferential operators has played an important role in many exciting and deep investigations into linear PDE. Over the past decade, this tool has also begun to yield interesting results in nonlinear PDE. This book is devoted to a summary and reconsideration of some used of pseudodifferential operator techniques in nonlinear PDE. The book should be of interest to graduate students, instructors, and researchers interested in partial differential equations, nonlinear analysis in classical mathematical physics and differential geometry, and in harmonic analysis.
Book Synopsis The Technique of Pseudodifferential Operators by : Heinz Otto Cordes
Download or read book The Technique of Pseudodifferential Operators written by Heinz Otto Cordes and published by Cambridge University Press. This book was released on 1995-02-23 with total page 398 pages. Available in PDF, EPUB and Kindle. Book excerpt: Pseudodifferential operators arise naturally in a solution of boundary problems for partial differential equations. The formalism of these operators serves to make the Fourier-Laplace method applicable for nonconstant coefficient equations. This book presents the technique of pseudodifferential operators and its applications, especially to the Dirac theory of quantum mechanics. The treatment uses 'Leibniz formulas' with integral remainders or as asymptotic series. While a pseudodifferential operator is commonly defined by an integral formula, it also may be described by invariance under action of a Lie group. The author discusses connections to the theory of C*-algebras, invariant algebras of pseudodifferential operators under hyperbolic evolution, and the relation of the hyperbolic theory to the propagation of maximal ideals. The Technique of Pseudodifferential Operators will be of particular interest to researchers in partial differential equations and mathematical physics.
Book Synopsis Operator Algebras, Toeplitz Operators and Related Topics by : Wolfram Bauer
Download or read book Operator Algebras, Toeplitz Operators and Related Topics written by Wolfram Bauer and published by Springer Nature. This book was released on 2020-09-01 with total page 467 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Pseudodifferential Equations Over Non-Archimedean Spaces by : W. A. Zúñiga-Galindo
Download or read book Pseudodifferential Equations Over Non-Archimedean Spaces written by W. A. Zúñiga-Galindo and published by Springer. This book was released on 2017-01-08 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt: Focusing on p-adic and adelic analogues of pseudodifferential equations, this monograph presents a very general theory of parabolic-type equations and their Markov processes motivated by their connection with models of complex hierarchic systems. The Gelfand-Shilov method for constructing fundamental solutions using local zeta functions is developed in a p-adic setting and several particular equations are studied, such as the p-adic analogues of the Klein-Gordon equation. Pseudodifferential equations for complex-valued functions on non-Archimedean local fields are central to contemporary harmonic analysis and mathematical physics and their theory reveals a deep connection with probability and number theory. The results of this book extend and complement the material presented by Vladimirov, Volovich and Zelenov (1994) and Kochubei (2001), which emphasize spectral theory and evolution equations in a single variable, and Albeverio, Khrennikov and Shelkovich (2010), which deals mainly with the theory and applications of p-adic wavelets.
Book Synopsis Pseudo-Differential Operators by : Hans G. Feichtinger
Download or read book Pseudo-Differential Operators written by Hans G. Feichtinger and published by Springer. This book was released on 2008-08-15 with total page 214 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Complex Analysis in Number Theory by : Anatoly A. Karatsuba
Download or read book Complex Analysis in Number Theory written by Anatoly A. Karatsuba and published by CRC Press. This book was released on 1994-11-22 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book examines the application of complex analysis methods to the theory of prime numbers. In an easy to understand manner, a connection is established between arithmetic problems and those of zero distribution for special functions. Main achievements in this field of mathematics are described. Indicated is a connection between the famous Riemann zeta-function and the structure of the universe, information theory, and quantum mechanics. The theory of Riemann zeta-function and, specifically, distribution of its zeros are presented in a concise and comprehensive way. The full proofs of some modern theorems are given. Significant methods of the analysis are also demonstrated as applied to fundamental problems of number theory.
Book Synopsis Singular Ordinary Differential Operators and Pseudodifferential Equations by : Johannes Elschner
Download or read book Singular Ordinary Differential Operators and Pseudodifferential Equations written by Johannes Elschner and published by Springer. This book was released on 2006-11-14 with total page 199 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Additive Theory of Prime Numbers by : Luogeng Hua
Download or read book Additive Theory of Prime Numbers written by Luogeng Hua and published by American Mathematical Soc.. This book was released on 2009-12-04 with total page 206 pages. Available in PDF, EPUB and Kindle. Book excerpt: Loo-Keng Hua was a master mathematician, best known for his work using analytic methods in number theory. In particular, Hua is remembered for his contributions to Waring's Problem and his estimates of trigonometric sums. Additive Theory of Prime Numbers is an exposition of the classic methods as well as Hua's own techniques, many of which have now also become classic. An essential starting point is Vinogradov's mean-value theorem for trigonometric sums, which Hua usefully rephrases and improves. Hua states a generalized version of the Waring-Goldbach problem and gives asymptotic formulas for the number of solutions in Waring's Problem when the monomial $x^k$ is replaced by an arbitrary polynomial of degree $k$. The book is an excellent entry point for readers interested in additive number theory. It will also be of value to those interested in the development of the now classic methods of the subject.
Book Synopsis Pseudodifferential Operators and Spectral Theory by : M.A. Shubin
Download or read book Pseudodifferential Operators and Spectral Theory written by M.A. Shubin and published by Springer Science & Business Media. This book was released on 2001-07-03 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the second edition of Shubin's classical book. It provides an introduction to the theory of pseudodifferential operators and Fourier integral operators from the very basics. The applications discussed include complex powers of elliptic operators, Hörmander asymptotics of the spectral function and eigenvalues, and methods of approximate spectral projection. Exercises and problems are included to help the reader master the essential techniques. The book is written for a wide audience of mathematicians, be they interested students or researchers.
Book Synopsis Analytic Number Theory: An Introductory Course by : Bateman Paul Trevier
Download or read book Analytic Number Theory: An Introductory Course written by Bateman Paul Trevier and published by World Scientific. This book was released on 2004-09-07 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: This valuable book focuses on a collection of powerful methods of analysis that yield deep number-theoretical estimates. Particular attention is given to counting functions of prime numbers and multiplicative arithmetic functions. Both real variable (”elementary”) and complex variable (”analytic”) methods are employed. The reader is assumed to have knowledge of elementary number theory (abstract algebra will also do) and real and complex analysis. Specialized analytic techniques, including transform and Tauberian methods, are developed as needed.Comments and corrigenda for the book are found at www.math.uiuc.edu/~diamond/.
Book Synopsis International Conference on Analytic Methods in Number Theory and Analysis, Moscow, 14-19 September 1981 by :
Download or read book International Conference on Analytic Methods in Number Theory and Analysis, Moscow, 14-19 September 1981 written by and published by American Mathematical Soc.. This book was released on 1986 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
