A Method Of Averaging In The Theory Of Orthogonal Series And Some Problems In The Theory Of Bases
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Probability Theory Function Theory Mechanics
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Author : I︠U︡riĭ Vasilʹevich Prokhorov
language : en
Publisher: American Mathematical Soc.
Release Date : 1990
Probability Theory Function Theory Mechanics written by I︠U︡riĭ Vasilʹevich Prokhorov 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 1990 with Mathematics categories.
This is a translation of the fifth and final volume in a special cycle of publications in commemoration of the 50th anniversary of the Steklov Mathematical Institute of the Academy of Sciences in the USSR. The purpose of the special cycle was to present surveys of work on certain important trends and problems pursued at the Institute. Because the choice of the form and character of the surveys were left up to the authors, the surveys do not necessarily form a comprehensive overview, but rather represent the authors' perspectives on the important developments.
A Method Of Averaging In The Theory Of Orthogonal Series And Some Problems In The Theory Of Bases
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Author : Sergeĭ Viktorovich Bochkarev
language : en
Publisher: American Mathematical Soc.
Release Date : 1980
A Method Of Averaging In The Theory Of Orthogonal Series And Some Problems In The Theory Of Bases written by Sergeĭ Viktorovich Bochkarev 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 1980 with Mathematics categories.
"Investigate various forms of convergence of Fourier series in general orthonormal systems as well as certain problems in the theory of bases" -- Introduction.
Orthogonal Series And Approximation Of Functions
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Author : Sergej Michajlovic Nikol'skij
language : en
Publisher: American Mathematical Soc.
Release Date : 1985-12-15
Orthogonal Series And Approximation Of Functions written by Sergej Michajlovic Nikol'skij 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 1985-12-15 with Mathematics categories.
Orthogonal Series
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Author : B. S. Kashin
language : en
Publisher: American Mathematical Soc.
Release Date : 2005-04-26
Orthogonal Series written by B. S. Kashin 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 2005-04-26 with Mathematics categories.
Introductory concepts and some general results Independent functions and their first applications The Haar system Some results on the trigonometric and Walsh systems The Hilbert transform and some function spaces The Faber-Schauder and Franklin systems Orthogonalization and factorization theorems Theorems on the convergence of general orthogonal series General theorems on the divergence of orthogonal series Some theorems on the representation of functions by orthogonal series
Harmonic Analysis On The Real Line
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Author : Elijah Liflyand
language : en
Publisher: Springer Nature
Release Date : 2021-09-27
Harmonic Analysis On The Real Line written by Elijah Liflyand and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-09-27 with Mathematics categories.
This book sketches a path for newcomers into the theory of harmonic analysis on the real line. It presents a collection of both basic, well-known and some less known results that may serve as a background for future research around this topic. Many of these results are also a necessary basis for multivariate extensions. An extensive bibliography, as well as hints to open problems are included. The book can be used as a skeleton for designing certain special courses, but it is also suitable for self-study.
Banach Spaces For Analysts
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Author : P. Wojtaszczyk
language : en
Publisher: Cambridge University Press
Release Date : 1996-08
Banach Spaces For Analysts written by P. Wojtaszczyk and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-08 with Mathematics categories.
This book is intended to be used with graduate courses in Banach space theory.
Selected Papers
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Author : Joseph L. Walsh
language : en
Publisher: Springer Science & Business Media
Release Date : 2000-02-11
Selected Papers written by Joseph L. Walsh 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 2000-02-11 with Mathematics categories.
This volume is a selection from the 281 published papers of Joseph Leonard Walsh, former US Naval Officer and professor at University of Maryland and Harvard University. The nine broad sections are ordered following the evolution of his work. Commentaries and discussions of subsequent development are appended to most of the sections. Also included is one of Walsh's most influential works, "A closed set of normal orthogonal function," which introduced what is now known as "Walsh Functions".
Conjugate Duality And The Exponential Fourier Spectrum
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Author : W. Britton
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Conjugate Duality And The Exponential Fourier Spectrum written by W. Britton 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 2012-12-06 with Mathematics categories.
For some fields such as econometrics (Shore, 1980), oil prospecting (Claerbout, 1976), speech recognition (Levinson and Lieberman, 1981), satellite monitoring (Lavergnat et al., 1980), epilepsy diagnosis (Gersch and Tharp, 1977), and plasma physics (Bloomfield, 1976), there is a need to obtain an estimate of the spectral density (when it exists) in order to gain at least a crude understanding of the frequency content of time series data. An outstanding tutorial on the classical problem of spectral density estimation is given by Kay and Marple (1981). For an excellent collection of fundamental papers dealing with modern spec tral density estimation as well as an extensive bibliography on other fields of application, see Childers (1978). To devise a high-performance sample spectral density estimator, one must develop a rational basis for its construction, provide a feasible algorithm, and demonstrate its performance with respect to prescribed criteria. An algorithm is certainly feasible if it can be implemented on a computer, possesses computational efficiency (as measured by compu tational complexity analysis), and exhibits numerical stability. An estimator shows high performance if it is insensitive to violations of its underlying assumptions (i.e., robust), consistently shows excellent frequency resolutipn under realistic sample sizes and signal-to-noise power ratios, possesses a demonstrable numerical rate of convergence to the true population spectral density, and/or enjoys demonstrable asymp totic statistical properties such as consistency and efficiency.
Decay Of The Fourier Transform
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Author : Alex Iosevich
language : en
Publisher: Springer
Release Date : 2014-10-01
Decay Of The Fourier Transform written by Alex Iosevich and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-10-01 with Mathematics categories.
The Plancherel formula says that the L^2 norm of the function is equal to the L^2 norm of its Fourier transform. This implies that at least on average, the Fourier transform of an L^2 function decays at infinity. This book is dedicated to the study of the rate of this decay under various assumptions and circumstances, far beyond the original L^2 setting. Analytic and geometric properties of the underlying functions interact in a seamless symbiosis which underlines the wide range influences and applications of the concepts under consideration.
Commutative Harmonic Analysis I
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Author : V.P. Khavin
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Commutative Harmonic Analysis I written by V.P. Khavin 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 volume is the first in the series devoted to the commutative harmonic analysis, a fundamental part of the contemporary mathematics. The fundamental nature of this subject, however, has been determined so long ago, that unlike in other volumes of this publication, we have to start with simple notions which have been in constant use in mathematics and physics. Planning the series as a whole, we have assumed that harmonic analysis is based on a small number of axioms, simply and clearly formulated in terms of group theory which illustrate its sources of ideas. However, our subject cannot be completely reduced to those axioms. This part of mathematics is so well developed and has so many different sides to it that no abstract scheme is able to cover its immense concreteness completely. In particular, it relates to an enormous stock of facts accumulated by the classical "trigonometric" harmonic analysis. Moreover, subjected to a general mathematical tendency of integration and diffusion of conventional intersubject borders, harmonic analysis, in its modem form, more and more rests on non-translation invariant constructions. For example, one ofthe most signifi cant achievements of latter decades, which has substantially changed the whole shape of harmonic analysis, is the penetration in this subject of subtle techniques of singular integral operators.