Download or read book Transmutation Operators and Mean periodic Functions Associated with Differential Operators written by K. Trimèche and published by CRC Press. This book was released on 1988 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Transmutation Operators and Applications written by Vladislav V. Kravchenko and published by Springer Nature. This book was released on 2020-04-11 with total page 685 pages. Available in PDF, EPUB and Kindle. Book excerpt: Transmutation operators in differential equations and spectral theory can be used to reveal the relations between different problems, and often make it possible to transform difficult problems into easier ones. Accordingly, they represent an important mathematical tool in the theory of inverse and scattering problems, of ordinary and partial differential equations, integral transforms and equations, special functions, harmonic analysis, potential theory, and generalized analytic functions. This volume explores recent advances in the construction and applications of transmutation operators, while also sharing some interesting historical notes on the subject.
Download or read book Generalized Wavelets and Hypergroups written by Khalifa Trimeche and published by Routledge. This book was released on 2019-01-22 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: Wavelets have recently been enjoying a period of popularity and rapid growth, and the influence of wavelet methods now extends well beyond mathematics into a number of practical fields, including statistics. The theory of hypergroups can be traced back to the turn of the century, and following its formalization in the early 1970s, the area has now
Download or read book Special Functions Proceedings Of The International Workshop written by Charles F Dunki and published by World Scientific. This book was released on 2000-10-27 with total page 451 pages. Available in PDF, EPUB and Kindle. Book excerpt: Special functions and q-series are currently very active areas of research which overlap with many other areas of mathematics, such as representation theory, classical and quantum groups, affine Lie algebras, number theory, harmonic analysis, and mathematical physics. This book presents the state-of-the-art of the subject and its applications.
Download or read book Proceedings of the International Workshop Special Functions written by Charles F. Dunkl and published by World Scientific. This book was released on 2000 with total page 460 pages. Available in PDF, EPUB and Kindle. Book excerpt: Special functions and q-series are currently very active areas of research which overlap with many other areas of mathematics, such as representation theory, classical and quantum groups, affine Lie algebras, number theory, harmonic analysis, and mathematical physics. This book presents the state-of-the-art of the subject and its applications.
Download or read book Fundamental Solutions of Linear Partial Differential Operators written by Norbert Ortner and published by Springer. This book was released on 2015-08-05 with total page 407 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph provides the theoretical foundations needed for the construction of fundamental solutions and fundamental matrices of (systems of) linear partial differential equations. Many illustrative examples also show techniques for finding such solutions in terms of integrals. Particular attention is given to developing the fundamentals of distribution theory, accompanied by calculations of fundamental solutions. The main part of the book deals with existence theorems and uniqueness criteria, the method of parameter integration, the investigation of quasihyperbolic systems by means of Fourier and Laplace transforms, and the representation of fundamental solutions of homogeneous elliptic operators with the help of Abelian integrals. In addition to rigorous distributional derivations and verifications of fundamental solutions, the book also shows how to construct fundamental solutions (matrices) of many physically relevant operators (systems), in elasticity, thermoelasticity, hexagonal/cubic elastodynamics, for Maxwell’s system and others. The book mainly addresses researchers and lecturers who work with partial differential equations. However, it also offers a valuable resource for students with a solid background in vector calculus, complex analysis and functional analysis.
Download or read book Operator Theory Pseudo Differential Equations and Mathematical Physics written by Yuri I. Karlovich and published by Springer Science & Business Media. This book was released on 2012-10-30 with total page 425 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is a collection of papers devoted to the 70th birthday of Professor Vladimir Rabinovich. The opening article (by Stefan Samko) includes a short biography of Vladimir Rabinovich, along with some personal recollections and bibliography of his work. It is followed by twenty research and survey papers in various branches of analysis (pseudodifferential operators and partial differential equations, Toeplitz, Hankel, and convolution type operators, variable Lebesgue spaces, etc.) close to Professor Rabinovich's research interests. Many of them are written by participants of the International workshop “Analysis, Operator Theory, and Mathematical Physics” (Ixtapa, Mexico, January 23–27, 2012) having a long history of scientific collaboration with Vladimir Rabinovich, and are partially based on the talks presented there.The volume will be of great interest to researchers and graduate students in differential equations, operator theory, functional and harmonic analysis, and mathematical physics.
Download or read book Direct and Inverse Sturm Liouville Problems written by Vladislav V. Kravchenko and published by Springer Nature. This book was released on 2020-07-28 with total page 155 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to the most recent developments in the theory and practice of direct and inverse Sturm-Liouville problems on finite and infinite intervals. A universal approach for practical solving of direct and inverse spectral and scattering problems is presented, based on the notion of transmutation (transformation) operators and their efficient construction. Analytical representations for solutions of Sturm-Liouville equations as well as for the integral kernels of the transmutation operators are derived in the form of functional series revealing interesting special features and lending themselves to direct and simple numerical solution of a wide variety of problems. The book is written for undergraduate and graduate students, as well as for mathematicians, physicists and engineers interested in direct and inverse spectral problems.
Download or read book Harmonic Analysis of Probability Measures on Hypergroups written by Walter R. Bloom and published by Walter de Gruyter. This book was released on 2011-04-20 with total page 609 pages. Available in PDF, EPUB and Kindle. Book excerpt: The series is devoted to the publication of monographs and high-level textbooks in mathematics, mathematical methods and their applications. Apart from covering important areas of current interest, a major aim is to make topics of an interdisciplinary nature accessible to the non-specialist. The works in this series are addressed to advanced students and researchers in mathematics and theoretical physics. In addition, it can serve as a guide for lectures and seminars on a graduate level. The series de Gruyter Studies in Mathematics was founded ca. 30 years ago by the late Professor Heinz Bauer and Professor Peter Gabriel with the aim to establish a series of monographs and textbooks of high standard, written by scholars with an international reputation presenting current fields of research in pure and applied mathematics. While the editorial board of the Studies has changed with the years, the aspirations of the Studies are unchanged. In times of rapid growth of mathematical knowledge carefully written monographs and textbooks written by experts are needed more than ever, not least to pave the way for the next generation of mathematicians. In this sense the editorial board and the publisher of the Studies are devoted to continue the Studies as a service to the mathematical community. Please submit any book proposals to Niels Jacob.
Download or read book Probability Measures on Groups X written by H. Heyer and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 491 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present volume contains the transactions of the lOth Oberwolfach Conference on "Probability Measures on Groups". The series of these meetings inaugurated in 1970 by L. Schmetterer and the editor is devoted to an intensive exchange of ideas on a subject which developed from the relations between various topics of mathematics: measure theory, probability theory, group theory, harmonic analysis, special functions, partial differential operators, quantum stochastics, just to name the most significant ones. Over the years the fruitful interplay broadened in various directions: new group-related structures such as convolution algebras, generalized translation spaces, hypercomplex systems, and hypergroups arose from generalizations as well as from applications, and a gradual refinement of the combinatorial, Banach-algebraic and Fourier analytic methods led to more precise insights into the theory. In a period of highest specialization in scientific thought the separated minds should be reunited by actively emphasizing similarities, analogies and coincidences between ideas in their fields of research. Although there is no real separation between one field and another - David Hilbert denied even the existence of any difference between pure and applied mathematics - bridges between probability theory on one side and algebra, topology and geometry on the other side remain absolutely necessary. They provide a favorable ground for the communication between apparently disjoint research groups and motivate the framework of what is nowadays called "Structural probability theory".
Download or read book Several Complex Variables V written by G.M. Khenkin and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume of the Encyclopaedia contains three contributions in the field of complex analysis; on mean periodicity and convolutionequations, Yang-Mills fields and the Radon-Penrose transform, and stringtheory. It is immensely useful to graduate students and researchers in complex analysis, differential geometry, quantum field theory, string theory and general relativity.
Download or read book Generalized Harmonic Analysis and Wavelet Packets written by Khalifa Trimeche and published by CRC Press. This book was released on 2001-03-07 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book presents a more comprehensive treatment of transmutation operators associated with the Bessel operator, and explores many of their properties. They are fundamental in the complete study of the Bessel harmonic analysis and the Bessel wavelet packets. Many applications of these theories and their generalizations have been injected throughout the text by way of a rich collection of problems and references. The results and methods in this book should be of interest to graduate and researchers working in special functions such as Fourier analysis, hypergroup and operator theories, differential equations, probability theory and mathematical physics. Background materials are given in adequate detail to enable a graduate student to proceed rapidly from the very basics of the frontier of research in the area of generalized harmonic analysis and wavelets.
Download or read book Transmutations Singular and Fractional Differential Equations with Applications to Mathematical Physics written by Elina Shishkina and published by Academic Press. This book was released on 2020-07-24 with total page 594 pages. Available in PDF, EPUB and Kindle. Book excerpt: Transmutations, Singular and Fractional Differential Equations with Applications to Mathematical Physics connects difficult problems with similar more simple ones. The book's strategy works for differential and integral equations and systems and for many theoretical and applied problems in mathematics, mathematical physics, probability and statistics, applied computer science and numerical methods. In addition to being exposed to recent advances, readers learn to use transmutation methods not only as practical tools, but also as vehicles that deliver theoretical insights. - Presents the universal transmutation method as the most powerful for solving many problems in mathematics, mathematical physics, probability and statistics, applied computer science and numerical methods - Combines mathematical rigor with an illuminating exposition full of historical notes and fascinating details - Enables researchers, lecturers and students to find material under the single "roof"
Download or read book Harmonic Analysis in Hypercomplex Systems written by Yu.M. Berezansky and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 494 pages. Available in PDF, EPUB and Kindle. Book excerpt: First works related to the topics covered in this book belong to J. Delsarte and B. M. Le vitan and appeared since 1938. In these works, the families of operators that generalize usual translation operators were investigated and the corresponding harmonic analysis was constructed. Later, starting from 1950, it was noticed that, in such constructions, an important role is played by the fact that the kernels of the corresponding convolutions of functions are nonnegative and by the properties of the normed algebras generated by these convolutions. That was the way the notion of hypercomplex system with continu ous basis appeared. A hypercomplex system is a normed algebra of functions on a locally compact space Q-the "basis" of this hypercomplex system. Later, similar objects, hypergroups, were introduced, which have complex-valued measures on Q as elements and convolution defined to be essentially the convolution of functionals and dual to the original convolution (if measures are regarded as functionals on the space of continuous functions on Q). However, until 1991, the time when this book was written in Russian, there were no monographs containing fundamentals of the theory (with an exception of a short section in the book by Yu. M. Berezansky and Yu. G. Kondratiev [BeKo]). The authors wanted to give an introduction to the theory and cover the most important subsequent results and examples.
Download or read book Applications of Hypergroups and Related Measure Algebras written by and published by American Mathematical Soc.. This book was released on 1995-02-28 with total page 458 pages. Available in PDF, EPUB and Kindle. Book excerpt: `The most important single thing about this conference was that it brought together for the first time representatives of all major groups of users of hypergroups. [They] talked to each other about how they were using hypergroups in fields as diverse as special functions, probability theory, representation theory, measure algebras, Hopf algebras, and Hecke algebras. This led to fireworks.' - from the Introduction. Hypergroups occur in a wide variety of contexts, and mathematicians the world over have been discovering this same mathematical structure hidden in very different applications. The diverse viewpoints on the subject have led to the need for a common perspective, if not a common theory. Presenting the proceedings of a Joint Summer Research Conference held in Seattle in the summer of 1993, this book will serve as a valuable starting point and reference tool for the wide range of users of hypergroups and make it easier for an even larger audience to use these structures in their work.
Download or read book Harmonic Analysis of Mean Periodic Functions on Symmetric Spaces and the Heisenberg Group written by Valery V. Volchkov and published by Springer Science & Business Media. This book was released on 2009-06-13 with total page 667 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of mean periodic functions is a subject which goes back to works of Littlewood, Delsarte, John and that has undergone a vigorous development in recent years. There has been much progress in a number of problems concerning local - pects of spectral analysis and spectral synthesis on homogeneous spaces. The study oftheseproblemsturnsouttobecloselyrelatedtoavarietyofquestionsinharmonic analysis, complex analysis, partial differential equations, integral geometry, appr- imation theory, and other branches of contemporary mathematics. The present book describes recent advances in this direction of research. Symmetric spaces and the Heisenberg group are an active ?eld of investigation at 2 the moment. The simplest examples of symmetric spaces, the classical 2-sphere S 2 and the hyperbolic plane H , play familiar roles in many areas in mathematics. The n Heisenberg groupH is a principal model for nilpotent groups, and results obtained n forH may suggest results that hold more generally for this important class of Lie groups. The purpose of this book is to develop harmonic analysis of mean periodic functions on the above spaces.
Download or read book Mathematical Reviews written by and published by . This book was released on 2004 with total page 1078 pages. Available in PDF, EPUB and Kindle. Book excerpt:
