Harmonic Analysis In Hypercomplex Systems
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Harmonic Analysis In Hypercomplex Systems
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Author : Yu.M. Berezansky
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
Harmonic Analysis In Hypercomplex Systems written by Yu.M. Berezansky 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 2013-06-29 with Mathematics categories.
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.
Harmonic Analysis In Hypercomplex Systems
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Author : Yu. M. Berezansky
language : en
Publisher:
Release Date : 2014-01-15
Harmonic Analysis In Hypercomplex Systems written by Yu. M. Berezansky and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.
Harmonic Analysis On Hypergroups Approximation And Stochastic Sequences
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Author : Rupert Lasser
language : en
Publisher: World Scientific
Release Date : 2022-12-06
Harmonic Analysis On Hypergroups Approximation And Stochastic Sequences written by Rupert Lasser and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-12-06 with Mathematics categories.
The book aims at giving a monographic presentation of the abstract harmonic analysis of hypergroups, while combining it with applied topics of spectral analysis, approximation by orthogonal expansions and stochastic sequences. Hypergroups are locally compact Hausdorff spaces equipped with a convolution, an involution and a unit element. Related algebraic structures had already been studied by Frobenius around 1900. Their axiomatic characterisation in harmonic analysis was later developed in the 1970s. Hypergoups naturally emerge in seemingly different application areas as time series analysis, probability theory and theoretical physics.The book presents harmonic analysis on commutative and polynomial hypergroups as well as weakly stationary random fields and sequences thereon. For polynomial hypergroups also difference equations and stationary sequences are considered. At greater extent than in the existing literature, the book compiles a rather comprehensive list of hypergroups, in particular of polynomial hypergroups. With an eye on readers at advanced undergraduate and graduate level, the proofs are generally worked out in careful detail. The bibliography is extensive.
Voronezh Winter Mathematical Schools
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Author : Peter Kuchment
language : en
Publisher: American Mathematical Soc.
Release Date : 1998
Voronezh Winter Mathematical Schools written by Peter Kuchment 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 1998 with Mathematics categories.
The Voronezh Winter Mathematical School was an annual event in the scientific life of the former Soviet Union for 25 years. Articles collected here are written by prominent mathematicians and former lecturers and participants of the school, covering a range of subjects in analysis and geometry. Specific topics include global analysis, harmonic analysis, function theory, dynamical systems, operator theory, mathematical physics, spectral theory, homogenization, algebraic geometry, differential geometry, and geometric analysis. For researchers and graduate students in analysis, geometry, and mathematical physics. No index. Annotation copyrighted by Book News, Inc., Portland, OR
Applications Of Hypergroups And Related Measure Algebras
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Author :
language : en
Publisher: American Mathematical Soc.
Release Date : 1995-02-28
Applications Of Hypergroups And Related Measure Algebras 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 1995-02-28 with Mathematics categories.
`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.
Parametric Lie Group Actions On Global Generalised Solutions Of Nonlinear Pdes
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Author : Elemer E. Rosinger
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Parametric Lie Group Actions On Global Generalised Solutions Of Nonlinear Pdes written by Elemer E. Rosinger 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 2013-03-09 with Mathematics categories.
This book presents global actions of arbitrary Lie groups on large classes of generalised functions by using a novel parametric approach. This new method extends and completes earlier results of the author and collaborators, in which global Lie group actions on generalised functions were only defined in the case of projectable or fibre-preserving Lie group actions. The parametric method opens the possibility of dealing with vastly larger classes of Lie semigroup actions which still transform solutions into solutions. These Lie semigroups can contain arbitrary noninvertible smooth mappings. Thus, they cannot be subsemigroups of Lie groups. Audience: This volume is addressed to graduate students and researchers involved in solving linear and nonlinear partial differential equations, and in particular, in dealing with the Lie group symmetries of their classical or generalised solutions.
Probability On Algebraic Structures
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Author : Gregory Budzban
language : en
Publisher: American Mathematical Soc.
Release Date : 2000
Probability On Algebraic Structures written by Gregory Budzban 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 2000 with Mathematics categories.
This volume presents results from an AMS Special Session held on the topic in Gainesville (FL). Papers included are written by an international group of well-known specialists who offer an important cross-section of current work in the field. In addition there are two expository papers that provide an avenue for non-specialists to comprehend problems in this area. The breadth of research in this area is evident by the variety of articles presented in the volume. Results concern probability on Lie groups and general locally compact groups. Generalizations of groups appear as hypergroups, abstract semigroups, and semigroups of matrices. Work on symmetric cones is included. Lastly, there are a number of articles on the current progress in constructing stochastic processes on quantum groups.
Harmonic Analysis Of Probability Measures On Hypergroups
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Author : Walter R. Bloom
language : en
Publisher: Walter de Gruyter
Release Date : 2011-04-20
Harmonic Analysis Of Probability Measures On Hypergroups written by Walter R. Bloom and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-04-20 with Mathematics categories.
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.
Structural Aspects In The Theory Of Probability
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Author : Herbert Heyer
language : en
Publisher: World Scientific
Release Date : 2004
Structural Aspects In The Theory Of Probability written by Herbert Heyer and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Business & Economics categories.
This book focuses on the algebraic-topological aspects of probabilitytheory, leading to a wider and deeper understanding of basic theorems, such as those on the structure of continuous convolution semigroupsand the corresponding processes with independent increments
Integration On Infinite Dimensional Surfaces And Its Applications
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Author : A. Uglanov
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
Integration On Infinite Dimensional Surfaces And Its Applications written by A. Uglanov 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 2013-06-29 with Mathematics categories.
It seems hard to believe, but mathematicians were not interested in integration problems on infinite-dimensional nonlinear structures up to 70s of our century. At least the author is not aware of any publication concerning this theme, although as early as 1967 L. Gross mentioned that the analysis on infinite dimensional manifolds is a field of research with rather rich opportunities in his classical work [2. This prediction was brilliantly confirmed afterwards, but we shall return to this later on. In those days the integration theory in infinite dimensional linear spaces was essentially developed in the heuristic works of RP. Feynman [1], I. M. Gelfand, A. M. Yaglom [1]). The articles of J. Eells [1], J. Eells and K. D. Elworthy [1], H. -H. Kuo [1], V. Goodman [1], where the contraction of a Gaussian measure on a hypersurface, in particular, was built and the divergence theorem (the Gauss-Ostrogradskii formula) was proved, appeared only in the beginning of the 70s. In this case a Gaussian specificity was essential and it was even pointed out in a later monograph of H. -H. Kuo [3] that the surface measure for the non-Gaussian case construction problem is not simple and has not yet been solved. A. V. Skorokhod [1] and the author [6,10] offered different approaches to such a construction. Some other approaches were offered later by Yu. L. Daletskii and B. D. Maryanin [1], O. G. Smolyanov [6], N. V.