Download or read book Classification and Approximation of Periodic Functions written by A.I. Stepanets and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 373 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph proposes a new classification of periodic functions, based on the concept of generalized derivative, defined by introducing multiplicators and shifts of the argument into the Fourier series of the original function. This approach permits the classification of a wide range of functions, including those of which the Fourier series may diverge in integral metric, smooth functions, and infinitely differentiable functions, including analytical and entire ones. These newly introduced classes are then investigated using the traditional problems of the theory of approximation. The results thus obtained offer a new way to look at classical statements for the approximation of differentiable functions, and suggest possibilities to discover new effects. Audience: valuable reading for experts in the field of mathematical analysis and researchers and graduate students interested in the applications of the theory of approximation and Fourier series.

Download or read book Approximation of Periodic Functions written by V. N. Temlyakov and published by . This book was released on 1993 with total page 438 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Collection of Papers from the All Union School on Function Theory written by S. B. Stechkin and published by American Mathematical Soc.. This book was released on 1991 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt: This collection consists of ten papers presented at the All-Union School on Function Theory, held in Dushanbe in August 1986, under the editor's guidance. The book encompasses a wide range of current directions in the metric theory of functions, the theory of approximation of functions, and related parts of mathematical analysis. The papers concern the following topics: extremal properties of functions, representation of functions by series, convergence of multiple Fourier series, approximation of functions by trigonometric polymonials in Lp-metrics, widths of classes of functions, approximation of functions by Fourier sums in systems of characters of zero-dimensional compact commutative groups, bilinear approximations of functions, the study of Tchebycheff sets in normed linear spaces, and spline approximation of functions of several variables. Among the results obtained are: new criteria for convexity of Tchebycheff sets in terms of continuity properties of the metric projection operator; conditions on the character of integrability of a periodic function of several variables under which its Fourier series converges to it in measure; a characterization of representation systems for symmetric spaces in which there are no nonzero continuous functionals.

Download or read book Methods of Approximation Theory written by Alexander I. Stepanets and published by V.S.P. International Science. This book was released on 2005 with total page 919 pages. Available in PDF, EPUB and Kindle. Book excerpt: The key point of the monograph is the classification of periodic functions introduced by the author and developed methods that enable one to solve, within the framework of a common approach, traditional problems of approximation theory for large collections of periodic functions. The main results are fairly complete and are presented in the form of either exact or asymptotically exact equalities. The present monograph is, in many respects, a store of knowledge accumulated in approximation theory by the beginning of the third millennium and serving for its further development.

Download or read book Methods of Approximation Theory written by and published by . This book was released on with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Approximation of periodic functions Pribli enie periodi eskich funkcij engl written by S. B. Stečkin and published by . This book was released on 1974 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Fourier Analysis and Approximation of Functions written by Roald M. Trigub and published by Springer Science & Business Media. This book was released on 2012-11-07 with total page 595 pages. Available in PDF, EPUB and Kindle. Book excerpt: In Fourier Analysis and Approximation of Functions basics of classical Fourier Analysis are given as well as those of approximation by polynomials, splines and entire functions of exponential type. In Chapter 1 which has an introductory nature, theorems on convergence, in that or another sense, of integral operators are given. In Chapter 2 basic properties of simple and multiple Fourier series are discussed, while in Chapter 3 those of Fourier integrals are studied. The first three chapters as well as partially Chapter 4 and classical Wiener, Bochner, Bernstein, Khintchin, and Beurling theorems in Chapter 6 might be interesting and available to all familiar with fundamentals of integration theory and elements of Complex Analysis and Operator Theory. Applied mathematicians interested in harmonic analysis and/or numerical methods based on ideas of Approximation Theory are among them. In Chapters 6-11 very recent results are sometimes given in certain directions. Many of these results have never appeared as a book or certain consistent part of a book and can be found only in periodics; looking for them in numerous journals might be quite onerous, thus this book may work as a reference source. The methods used in the book are those of classical analysis, Fourier Analysis in finite-dimensional Euclidean space Diophantine Analysis, and random choice.

Download or read book Methods of Approximation Theory written by Alexander I. Stepanets and published by Walter de Gruyter. This book was released on 2011-12-22 with total page 941 pages. Available in PDF, EPUB and Kindle. Book excerpt: The key point of the monograph is the classification of periodic functions introduced by the author and developed methods that enable one to solve, within the framework of a common approach, traditional problems of approximation theory for large collections of periodic functions. The main results are fairly complete and are presented in the form of either exact or asymptotically exact equalities. The present monograph is, in many respects, a store of knowledge accumulated in approximation theory by the beginning of the third millennium and serving for its further development.

Download or read book Trigonometric Sums and Their Applications written by Andrei Raigorodskii and published by Springer Nature. This book was released on 2020-03-11 with total page 313 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents in a unified manner both classic as well as modern research results devoted to trigonometric sums. Such sums play an integral role in the formulation and understanding of a broad spectrum of problems which range over surprisingly many and different research areas. Fundamental and new developments are presented to discern solutions to problems across several scientific disciplines. Graduate students and researchers will find within this book numerous examples and a plethora of results related to trigonometric sums through pure and applied research along with open problems and new directions for future research.

Download or read book The Gibbs Phenomenon in Fourier Analysis Splines and Wavelet Approximations written by A.J. Jerri and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 357 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book represents the first attempt at a unified picture for the pres ence of the Gibbs (or Gibbs-Wilbraham) phenomenon in applications, its analysis and the different methods of filtering it out. The analysis and filtering cover the familiar Gibbs phenomenon in Fourier series and integral representations of functions with jump discontinuities. In ad dition it will include other representations, such as general orthogonal series expansions, general integral transforms, splines approximation, and continuous as well as discrete wavelet approximations. The mate rial in this book is presented in a manner accessible to upperclassmen and graduate students in science and engineering, as well as researchers who may face the Gibbs phenomenon in the varied applications that in volve the Fourier and the other approximations of functions with jump discontinuities. Those with more advanced backgrounds in analysis will find basic material, results, and motivations from which they can begin to develop deeper and more general results. We must emphasize that the aim of this book (the first on the sUbject): to satisfy such a diverse audience, is quite difficult. In particular, our detailed derivations and their illustrations for an introductory book may very well sound repeti tive to the experts in the field who are expecting a research monograph. To answer the concern of the researchers, we can only hope that this book will prove helpful as a basic reference for their research papers.

Download or read book Elements of the General Theory of Optimal Algorithms written by Ivan V. Sergienko and published by Springer Nature. This book was released on 2022-01-11 with total page 387 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this monograph, the authors develop a methodology that allows one to construct and substantiate optimal and suboptimal algorithms to solve problems in computational and applied mathematics. Throughout the book, the authors explore well-known and proposed algorithms with a view toward analyzing their quality and the range of their efficiency. The concept of the approach taken is based on several theories (of computations, of optimal algorithms, of interpolation, interlination, and interflatation of functions, to name several). Theoretical principles and practical aspects of testing the quality of algorithms and applied software, are a major component of the exposition. The computer technology in construction of T-efficient algorithms for computing ε-solutions to problems of computational and applied mathematics, is also explored. The readership for this monograph is aimed at scientists, postgraduate students, advanced students, and specialists dealing with issues of developing algorithmic and software support for the solution of problems of computational and applied mathematics.

Download or read book Approximation of Periodic Functions written by S. B. Stechkin and published by American Mathematical Soc.. This book was released on 1974 with total page 144 pages. Available in PDF, EPUB and Kindle. Book excerpt: Papers and articles about periodic functions approximation.

Download or read book Investigations on the Theory of Functions of Several Real Variables and the Approximation of Functions written by Sergeĭ Lʹvovich Sobolev and published by . This book was released on 1987 with total page 398 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Translations Ser 2 159 Proceedings of the St Petersburg Mathematical Society 2 written by United States. Office of Naval Research and published by American Mathematical Soc.. This book was released on 1994-11-22 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains papers on a wide range of topics, including diophantine equations, algebraic number theory, ring theory, theory of functions of a real variable, partial differential equations, approximation of functions, differential geometry, computing theory, and statistical mechanics. The last three papers present historical perspectives on mathematics in St. Petersburg.

Download or read book 30 Years Review Of China s Science And Technology 1949 1979 written by and published by World Scientific. This book was released on 1982-01-01 with total page 325 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the 1st China's Science Yearbook published since 1949. It covers events, activities and progresses in various fields of science and technology from 1949 to 1979. Published in conjunction with Shanghai Scientific Publishing Co., it was compiled and edited by a research team from 'Nature Magazine', Shanghai, People's Republic of China.

Download or read book On the Degree of Approximation of Functions of 2 pi periodic Functions in C o 1 with Positive Linear Operators of the Jackson Type written by F. Schurer and published by . This book was released on 1977 with total page 96 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Statistics Data Mining and Machine Learning in Astronomy written by Željko Ivezić and published by Princeton University Press. This book was released on 2019-12-03 with total page 548 pages. Available in PDF, EPUB and Kindle. Book excerpt: "As telescopes, detectors, and computers grow ever more powerful, the volume of data at the disposal of astronomers and astrophysicists will enter the petabyte domain, providing accurate measurements for billions of celestial objects. This book provides a comprehensive and accessible introduction to the cutting-edge statistical methods needed to efficiently analyze complex data sets from astronomical surveys such as the Panoramic Survey Telescope and Rapid Response System, the Dark Energy Survey, and the upcoming Large Synoptic Survey Telescope. It serves as a practical handbook for graduate students and advanced undergraduates in physics and astronomy, and as an indispensable reference for researchers. The updates in this new edition will include fixing "code rot," correcting errata, and adding some new sections. In particular, the new sections include new material on deep learning methods, hierarchical Bayes modeling, and approximate Bayesian computation. Statistics, Data Mining, and Machine Learning in Astronomy presents a wealth of practical analysis problems, evaluates techniques for solving them, and explains how to use various approaches for different types and sizes of data sets. For all applications described in the book, Python code and example data sets are provided. The supporting data sets have been carefully selected from contemporary astronomical surveys (for example, the Sloan Digital Sky Survey) and are easy to download and use. The accompanying Python code is publicly available, well documented, and follows uniform coding standards. Together, the data sets and code enable readers to reproduce all the figures and examples, evaluate the methods, and adapt them to their own fields of interest"--