Transmutation Operators And Applications
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Author | : Vladislav V. Kravchenko |
Publisher | : Springer Nature |
Total Pages | : 685 |
Release | : 2020-04-11 |
Genre | : Mathematics |
ISBN | : 303035914X |
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.
Author | : R. Carroll |
Publisher | : Elsevier |
Total Pages | : 365 |
Release | : 2011-08-18 |
Genre | : Mathematics |
ISBN | : 008087228X |
Transmutation Theory and Applications
Author | : Elina Shishkina |
Publisher | : Academic Press |
Total Pages | : 594 |
Release | : 2020-07-24 |
Genre | : Mathematics |
ISBN | : 0128204079 |
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"
Author | : Marek Ptak |
Publisher | : Springer Nature |
Total Pages | : 423 |
Release | : |
Genre | : |
ISBN | : 3031506138 |
Author | : Vladislav V. Kravchenko |
Publisher | : Springer Nature |
Total Pages | : 155 |
Release | : 2020-07-28 |
Genre | : Mathematics |
ISBN | : 3030478491 |
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.
Author | : |
Publisher | : American Mathematical Soc. |
Total Pages | : 458 |
Release | : 1995-02-28 |
Genre | : Mathematics |
ISBN | : 0821802976 |
`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.
Author | : K. Trimèche |
Publisher | : |
Total Pages | : 300 |
Release | : 1988 |
Genre | : Differential operators |
ISBN | : |
Author | : Virginia S Kiryakova |
Publisher | : CRC Press |
Total Pages | : 412 |
Release | : 1993-12-27 |
Genre | : Mathematics |
ISBN | : 9780582219779 |
In this volume various applications are discussed, in particular to the hyper-Bessel differential operators and equations, Dzrbashjan-Gelfond-Leontiev operators and Borel type transforms, convolutions, new representations of hypergeometric functions, solutions to classes of differential and integral equations, transmutation method, and generalized integral transforms. Some open problems are also posed. This book is intended for graduate and post-graduate students, lecturers, researchers and others working in applied mathematical analysis, mathematical physics and related disciplines.
Author | : Valery V. Volchkov |
Publisher | : Springer Science & Business Media |
Total Pages | : 667 |
Release | : 2009-06-13 |
Genre | : Mathematics |
ISBN | : 1848825331 |
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.
Author | : A Okay Celebi |
Publisher | : World Scientific |
Total Pages | : 877 |
Release | : 2009-01-13 |
Genre | : Mathematics |
ISBN | : 9814469114 |
The ISAAC (International Society for Analysis, its Applications and Computation) Congress, which has been held every second year since 1997, covers the major progress in analysis, applications and computation in recent years. In this proceedings volume, plenary lectures highlight the recent research results, while 17 sessions organized by well-known specialists reflect the state of the art of important subfields. This volume concentrates on partial differential equations, function spaces, operator theory, integral transforms and equations, potential theory, complex analysis and generalizations, inverse problems, functional differential and difference equations and integrable systems.