Download or read book The Theory of Ultraspherical Multipliers written by William Carroll Connett and published by American Mathematical Soc.. This book was released on 1977 with total page 100 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many multiplier theorems of Fourier analysis have analogs for ultraspherical expansions. But what was a single theorem in the Fourier setting becomes an entire family of theorems in this more general setting. The problem solved in this paper is that of organizing the children of the Fourier theorems, and many new theorems besides, into a coherent theory. The most critical step in this organization is identifying a family of Banach spaces which include the sequences described in the classical multiplier theorems as special cases. Once this family is found, the next step is to develop the methods of interpolation necessary to show that this family forms a scale of spaces--in the sense that if two spaces in the family act as multipliers on L[superscript]p, then all spaces "between" these two spaces act as multipliers on L[superscript]p.

Download or read book Transplantation Theorems and Multiplier Theorems for Jacobi Series written by Benjamin Muckenhoupt and published by American Mathematical Soc.. This book was released on 1986 with total page 94 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Harmonic Analysis On Hypergroups Approximation And Stochastic Sequences written by Rupert Lasser and published by World Scientific. This book was released on 2022-12-06 with total page 621 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

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 Quantitative Approximation written by Ronald A. Devore and published by Academic Press. This book was released on 2014-05-10 with total page 337 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantitative Approximation provides information pertinent to nonlinear approximation, including rational approximation and optimal knot spline approximation. This book discusses spline approximation with the most emphasis on multivariate and knot independent questions. Organized into 26 chapters, this book begins with an overview of the inequality for the sharp function in terms of the maximal rearrangement. This text then examines the best co-approximation in a Hilbert space wherein the existence ad uniqueness sets are the closed flats. Other chapters consider the inverse of the coefficient matrix for the system satisfied by the B-spline coefficients of the cubic spline interpolant at knots. This book discusses as well the relationship between the structural properties of a function and its degree of approximation by rational functions. The final chapter deals with the problem of existence of continuous selections for metric projections and provides a solution for this problem. This book is a valuable resource for mathematicians.

Download or read book Canadian Journal of Mathematics written by and published by . This book was released on 1977-12 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Lie Groups and Lie Algebras written by B.P. Komrakov and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 442 pages. Available in PDF, EPUB and Kindle. Book excerpt: This collection contains papers conceptually related to the classical ideas of Sophus Lie (i.e., to Lie groups and Lie algebras). Obviously, it is impos sible to embrace all such topics in a book of reasonable size. The contents of this one reflect the scientific interests of those authors whose activities, to some extent at least, are associated with the International Sophus Lie Center. We have divided the book into five parts in accordance with the basic topics of the papers (although it can be easily seen that some of them may be attributed to several parts simultaneously). The first part (quantum mathematics) combines the papers related to the methods generated by the concepts of quantization and quantum group. The second part is devoted to the theory of hypergroups and Lie hypergroups, which is one of the most important generalizations of the classical concept of locally compact group and of Lie group. A natural harmonic analysis arises on hypergroups, while any abstract transformation of Fourier type is gen erated by some hypergroup (commutative or not). Part III contains papers on the geometry of homogeneous spaces, Lie algebras and Lie superalgebras. Classical problems of the representation theory for Lie groups, as well as for topological groups and semigroups, are discussed in the papers of Part IV. Finally, the last part of the collection relates to applications of the ideas of Sophus Lie to differential equations.

Download or read book Convolutional Representations of Commutants and Multipliers written by Nikolai Bozhinov and published by . This book was released on 1988 with total page 318 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Multipliers for C alpha Bounded Fourier Expansions in Banach Spaces and Approximation Theory written by W. Trebels and published by Springer. This book was released on 2006-11-15 with total page 110 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Hypersingular Integrals and Their Applications written by Stefan Samko and published by CRC Press. This book was released on 2001-10-25 with total page 382 pages. Available in PDF, EPUB and Kindle. Book excerpt: Hypersingular integrals arise as constructions inverse to potential-type operators and are realized by the methods of regularization and finite differences. This volume develops these approaches in a comprehensive treatment of hypersingular integrals and their applications. The author is a renowned expert on the topic. He explains the basics before building more sophisticated ideas, and his discussions include a description of hypersingular integrals as they relate to functional spaces. Hypersingular Integrals and Their Applications also presents recent results and applications that will prove valuable to graduate students and researchers working in mathematical analysis.

Download or read book Fourier Series in Orthogonal Polynomials written by Boris Osilenker and published by World Scientific. This book was released on 1999 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a systematic coarse on general orthogonal polynomials and Fourie series in orthogonal polynomials. It consists of six chapters. Chapter 1 deals in essence with standard results from the university course on the function theory of a real variable and on functional analysis. Chapter 2 contains the classical results about the orthogonal polynomials (some properties, classical Jacobi polynomials and the criteria of boundedness). The main subject of the book is Fourier series in general orthogonal polynomials. Chapters 3 and 4 are devoted to some results in this topic (classical results about convergence and summability of Fourier series in L(2)micro; summability almost everywhere by the Cesaro means and the Poisson-Abel method for Fourier polynomial series are the subject of Chapters 4 and 5). The last chapter contains some estimates regarding the generalized shift operator and the generalized product formula, associated with general orthogonal polynomials. The starting point of the technique in Chapters 4 and 5 is the representations of bilinear and trilinear forms obtained by the author. The results obtained in these two chapters are new ones. Chapters 2 and 3 (and part of Chapter 1) will be useful to postgraduate students, and one can choose them for treatment. This book is intended for researchers (mathematicians and physicists) whose work involves function theory, functional analysis, harmonic analysis and approximation theory.

Download or read book Mathematics of Computation written by and published by . This book was released on 1978 with total page 694 pages. Available in PDF, EPUB and Kindle. Book excerpt: Original articles on all aspects of numerical mathematics, book reviews, mathematical tables, and technical notes. Covers advances in numerical analysis, application of computer methods, high speed calculating, and other aids to computation.

Download or read book Studia mathematica written by and published by . This book was released on 1980 with total page 668 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Acta Scientiarum Mathematicarum written by József Attila Tudományegyetem and published by . This book was released on 1995 with total page 838 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Transactions of the American Mathematical Society written by American Mathematical Society and published by . This book was released on 1979 with total page 1236 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Library of Congress Catalogs written by Library of Congress and published by . This book was released on 1978 with total page 802 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Topics in Fourier Analysis and Function Spaces written by Hans-Jurgen Schmeisser and published by . This book was released on 1987-03-11 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: A book dealing with several classes of Besov-Hardy-Sobolev function spaces on the Euclidean n-space and the n-torus. Periodic, weighted and anisotropic spaces are discussed, as well as spaces in which properties of dominating mixed smoothness predominate.