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Author : Antoni Zygmund
Publisher : Cambridge University Press
Page : 784 pages
File Size : 49,6 Mb
Release : 2002
Category : Mathematics
ISBN : 0521890535
Both volumes of classic text on trigonometric series, with a foreword by Robert Fefferman.
Author : Antoni Zygmund
Publisher : Unknown
Page : 747 pages
File Size : 47,6 Mb
Release : 1988
Category : Fourier series
ISBN : 052135885X
Originally published in 1935, Professor Zygmund's Trigonometric Series rapidly established itself as a classic and has remained one of the most referenced works of mathematics ever since. Originally published separately, the two volumes were subsequently bound together as a single book. Volume I contains the basic material on trigonometric series and Fourier analysis, including the summability of Fourier series, special trigonometric series, complex methods in Fourier series, and Riemann's theory of trigonometric series. Volume II covers trigonometric interpolation, differentiation of series, convergence and summability, Fourier integrals and other advanced topics.
Author : N. K. Bary
Publisher : Elsevier
Page : 578 pages
File Size : 53,7 Mb
Release : 2014-05-12
Category : Mathematics
ISBN : 9781483224190
A Treatise on Trigonometric Series, Volume 1 deals comprehensively with the classical theory of Fourier series. This book presents the investigation of best approximations of functions by trigonometric polynomials. Organized into six chapters, this volume begins with an overview of the fundamental concepts and theorems in the theory of trigonometric series, which play a significant role in mathematics and in many of its applications. This text then explores the properties of the Fourier coefficient function and estimates the rate at which its Fourier coefficients tend to zero. Other chapters consider some tests for the convergence of a Fourier series at a given point. This book discusses as well the conditions under which the series does converge uniformly. The final chapter deals with adjustment of a summable function outside a given perfect set. This book is a valuable resource for advanced students and research workers. Mathematicians will also find this book useful.
Author : L. Zhizhiashvili
Publisher : Springer Science & Business Media
Page : 314 pages
File Size : 41,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789400902831
Research in the theory of trigonometric series has been carried out for over two centuries. The results obtained have greatly influenced various fields of mathematics, mechanics, and physics. Nowadays, the theory of simple trigonometric series has been developed fully enough (we will only mention the monographs by Zygmund [15, 16] and Bari [2]). The achievements in the theory of multiple trigonometric series look rather modest as compared to those in the one-dimensional case though multiple trigonometric series seem to be a natural, interesting and promising object of investigation. We should say, however, that the past few decades have seen a more intensive development of the theory in this field. To form an idea about the theory of multiple trigonometric series, the reader can refer to the surveys by Shapiro [1], Zhizhiashvili [16], [46], Golubov [1], D'yachenko [3]. As to monographs on this topic, only that ofYanushauskas [1] is known to me. This book covers several aspects of the theory of multiple trigonometric Fourier series: the existence and properties of the conjugates and Hilbert transforms of integrable functions; convergence (pointwise and in the LP-norm, p > 0) of Fourier series and their conjugates, as well as their summability by the Cesaro (C,a), a> -1, and Abel-Poisson methods; approximating properties of Cesaro means of Fourier series and their conjugates.
Author : Ralph Jeffery
Publisher : Unknown
Page : 52 pages
File Size : 50,8 Mb
Release : 1956-12-15
Category : Education
ISBN : UOM:39015015629275
A survey of some of the main-line developments in trigonometric series. It is an extension of a Presidential address to Section III of the Royal Society of Canada. Part I deals briefly, in chronological order, with the mathematical problems that arose out of trigonometric series and the interactions between these problems and general mathematical analysis. There is mention of the contributions of Euler, Daniel Bernoulli, d'Alembert, Fourier, Lagrange, Dirichlet. This is followed by a description of some of the problems still open at the end of the period covered by these men, and a description of the way these problems were later solved by Denjoy, by Zygmund and Marcinkiewicz, by Burkill and by James. Part II gives complete proofs of the results of the earlier period outlined in Part I, and concludes with the essential details of the approach of Denjoy and of James. Canadian Mathematical Congress Lecture Series, No. 2.
Author : I.P. Natanson
Publisher : Courier Dover Publications
Page : 545 pages
File Size : 45,8 Mb
Release : 2016-08-17
Category : Mathematics
ISBN : 9780486806433
Long out-of-print volume by a prominent Soviet mathematician presents a thorough examination of the theory of functions of a real variable. Intended for advanced undergraduates and graduate students of mathematics. 1955 and 1960 editions.
Author : Ali Taheri
Publisher : OUP Oxford
Page : 500 pages
File Size : 52,7 Mb
Release : 2015-07-30
Category : Mathematics
ISBN : 9780191047824
This is a book written primarily for graduate students and early researchers in the fields of Analysis and Partial Differential Equations (PDEs). Coverage of the material is essentially self-contained, extensive and novel with great attention to details and rigour. The strength of the book primarily lies in its clear and detailed explanations, scope and coverage, highlighting and presenting deep and profound inter-connections between different related and seemingly unrelated disciplines within classical and modern mathematics and above all the extensive collection of examples, worked-out and hinted exercises. There are well over 700 exercises of varying level leading the reader from the basics to the most advanced levels and frontiers of research. The book can be used either for independent study or for a year-long graduate level course. In fact it has its origin in a year-long graduate course taught by the author in Oxford in 2004-5 and various parts of it in other institutions later on. A good number of distinguished researchers and faculty in mathematics worldwide have started their research career from the course that formed the basis for this book.
Author : Robert L. Brabenec
Publisher : Cambridge University Press
Page : 256 pages
File Size : 52,8 Mb
Release : 2004
Category : Mathematics
ISBN : 0883857375
A collection of materials gathered by the author while teaching real analysis over a period of years.
Author : Nina Karlovna Bari
Publisher : Pergamon
Page : 590 pages
File Size : 44,9 Mb
Release : 1964
Category : Mathematics
ISBN : UOM:39015015629325
Author : William Chauvenet
Publisher : Unknown
Page : 268 pages
File Size : 46,9 Mb
Release : 1852
Category : Trigonometry
ISBN : STANFORD:36105046444605
Author : Morris Kline
Publisher : Oxford University Press
Page : 440 pages
File Size : 41,7 Mb
Release : 1990-03-01
Category : Mathematics
ISBN : 9780199840434
This comprehensive history traces the development of mathematical ideas and the careers of the men responsible for them. Volume 1 looks at the disciplines origins in Babylon and Egypt, the creation of geometry and trigonometry by the Greeks, and the role of mathematics in the medieval and early modern periods. Volume 2 focuses on calculus, the rise of analysis in the 19th century, and the number theories of Dedekind and Dirichlet. The concluding volume covers the revival of projective geometry, the emergence of abstract algebra, the beginnings of topology, and the influence of Godel on recent mathematical study.
Author : Sergeĭ Viktorovich Bochkarev
Publisher : American Mathematical Soc.
Page : 104 pages
File Size : 41,8 Mb
Release : 1980
Category : Mathematics
ISBN : 0821830457
"Investigate various forms of convergence of Fourier series in general orthonormal systems as well as certain problems in the theory of bases" -- Introduction.
Author : Bruce West,Mauro Bologna,Paolo Grigolini
Publisher : Springer Science & Business Media
Page : 376 pages
File Size : 43,7 Mb
Release : 2003-01-14
Category : Mathematics
ISBN : 0387955542
This text describes how fractal phenomena, both deterministic and random, change over time, using the fractional calculus. The intent is to identify those characteristics of complex physical phenomena that require fractional derivatives or fractional integrals to describe how the process changes over time. The discussion emphasizes the properties of physical phenomena whose evolution is best described using the fractional calculus, such as systems with long-range spatial interactions or long-time memory. In many cases, classic analytic function theory cannot serve for modeling complex phenomena; "Physics of Fractal Operators" shows how classes of less familiar functions, such as fractals, can serve as useful models in such cases. Because fractal functions, such as the Weierstrass function (long known not to have a derivative), do in fact have fractional derivatives, they can be cast as solutions to fractional differential equations. The traditional techniques for solving differential equations, including Fourier and Laplace transforms as well as Green's functions, can be generalized to fractional derivatives. Physics of Fractal Operators addresses a general strategy for understanding wave propagation through random media, the nonlinear response of complex materials, and the fluctuations of various forms of transport in heterogeneous materials. This strategy builds on traditional approaches and explains why the historical techniques fail as phenomena become more and more complicated.
Author : Morris Kline
Publisher : Oxford University Press
Page : 480 pages
File Size : 45,6 Mb
Release : 1990-03-01
Category : Mathematics
ISBN : 0199840423
This comprehensive history traces the development of mathematical ideas and the careers of the men responsible for them. Volume 1 looks at the disciplines origins in Babylon and Egypt, the creation of geometry and trigonometry by the Greeks, and the role of mathematics in the medieval and early modern periods. Volume 2 focuses on calculus, the rise of analysis in the 19th century, and the number theories of Dedekind and Dirichlet. The concluding volume covers the revival of projective geometry, the emergence of abstract algebra, the beginnings of topology, and the influence of Godel on recent mathematical study.
Author : Manfred Stoll
Publisher : CRC Press
Page : 501 pages
File Size : 47,6 Mb
Release : 2021-03-10
Category : Mathematics
ISBN : 9781000345148
This classic textbook has been used successfully by instructors and students for nearly three decades. This timely new edition offers minimal yet notable changes while retaining all the elements, presentation, and accessible exposition of previous editions. A list of updates is found in the Preface to this edition. This text is based on the author’s experience in teaching graduate courses and the minimal requirements for successful graduate study. The text is understandable to the typical student enrolled in the course, taking into consideration the variations in abilities, background, and motivation. Chapters one through six have been written to be accessible to the average student, w hile at the same time challenging the more talented student through the exercises. Chapters seven through ten assume the students have achieved some level of expertise in the subject. In these chapters, the theorems, examples, and exercises require greater sophistication and mathematical maturity for full understanding. In addition to the standard topics the text includes topics that are not always included in comparable texts. Chapter 6 contains a section on the Riemann-Stieltjes integral and a proof of Lebesgue’s t heorem providing necessary and sufficient conditions for Riemann integrability. Chapter 7 also includes a section on square summable sequences and a brief introduction to normed linear spaces. C hapter 8 contains a proof of the Weierstrass approximation theorem using the method of aapproximate identities. The inclusion of Fourier series in the text allows the student to gain some exposure to this important subject. The final chapter includes a detailed treatment of Lebesgue measure and the Lebesgue integral, using inner and outer measure. The exercises at the end of each section reinforce the concepts. Notes provide historical comments or discuss additional topics.