Weak Type Estimates for Cesaro Sums of Jacobi Polynomial Series
Weak Type Estimates for Cesaro Sums of Jacobi Polynomial Series

Author: Sagun Chanillo

Publisher: American Mathematical Soc.

Published: 1993

Total Pages: 105

ISBN-13: 0821825488

DOWNLOAD EBOOK

This work completely characterizes the behaviour of Cesaro means of any order of the Jacobi polynomials. In particular, pointwise estimates are derived for the Cesaro mean kernel. Complete answers are given for the convergence almost everywhere of partial sums of Cesaro means of functions belonging to the critical L ]p spaces. This characterization is deduced from weak type estimates for the maximal partial sum operator. The methods used are fairly general and should apply to other series of special functions.

Weak Type Estimates for Cesaro Sums of Jacobi Polynomial Series
Weak Type Estimates for Cesaro Sums of Jacobi Polynomial Series

Author: Sagun Chanillo

Publisher: Oxford University Press, USA

Published: 2014-08-31

Total Pages: 105

ISBN-13: 9781470400644

DOWNLOAD EBOOK

This work, intended for research mathematicians, completely characterizes the behavior of Cesaro means of any order of the Jacobi polynomials. In particular, pointwise estimates are derived for the Cesaro mean kernel. Complete answers are given for the convergence almost everywhere of partial sums of Cesaro means of functions belonging to the critical $L $ spaces. This characterization is deduced from weak type estimates for the maximal partial sum operator. The methods used are fairly general and should apply to other series of special functions.

Approximation Theory and Harmonic Analysis on Spheres and Balls
Approximation Theory and Harmonic Analysis on Spheres and Balls

Author: Feng Dai

Publisher: Springer Science & Business Media

Published: 2013-04-17

Total Pages: 447

ISBN-13: 1461466601

DOWNLOAD EBOOK

This monograph records progress in approximation theory and harmonic analysis on balls and spheres, and presents contemporary material that will be useful to analysts in this area. While the first part of the book contains mainstream material on the subject, the second and the third parts deal with more specialized topics, such as analysis in weight spaces with reflection invariant weight functions, and analysis on balls and simplexes. The last part of the book features several applications, including cubature formulas, distribution of points on the sphere, and the reconstruction algorithm in computerized tomography. This book is directed at researchers and advanced graduate students in analysis. Mathematicians who are familiar with Fourier analysis and harmonic analysis will understand many of the concepts that appear in this manuscript: spherical harmonics, the Hardy-Littlewood maximal function, the Marcinkiewicz multiplier theorem, the Riesz transform, and doubling weights are all familiar tools to researchers in this area.

Fourier Series In Orthogonal Polynomials
Fourier Series In Orthogonal Polynomials

Author: Boris Osilenker

Publisher: World Scientific

Published: 1999-04-01

Total Pages: 295

ISBN-13: 9814495220

DOWNLOAD EBOOK

This book presents a systematic course on general orthogonal polynomials and Fourier 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 L2μ; 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, mechanicians and physicists) whose work involves function theory, functional analysis, harmonic analysis and approximation theory.

Handbook of Analytic Computational Methods in Applied Mathematics
Handbook of Analytic Computational Methods in Applied Mathematics

Author: George Anastassiou

Publisher: CRC Press

Published: 2019-06-03

Total Pages: 682

ISBN-13: 0429525117

DOWNLOAD EBOOK

Working computationally in applied mathematics is the very essence of dealing with real-world problems in science and engineering. Approximation theory-on the borderline between pure and applied mathematics- has always supplied some of the most innovative ideas, computational methods, and original approaches to many types of problems. The f

Prime Ideals in Skew and $q$-Skew Polynomial Rings
Prime Ideals in Skew and $q$-Skew Polynomial Rings

Author: K. R. Goodearl

Publisher: American Mathematical Soc.

Published: 1994

Total Pages: 118

ISBN-13: 0821825836

DOWNLOAD EBOOK

New methods are developed to describe prime ideals in skew polynomial rings [italic capital]S = [italic capital]R[[italic]y; [lowercase Greek]Tau, [lowercase Greek]Delta]], for automorphisms [lowercase Greek]Tau and [lowercase Greek]Tau-derivations [lowercase Greek]Delta] of a noetherian coefficient ring [italic capital]R.

Extensions of the Jacobi Identity for Vertex Operators, and Standard $A^{(1)}_1$-Modules
Extensions of the Jacobi Identity for Vertex Operators, and Standard $A^{(1)}_1$-Modules

Author: Cristiano Husu

Publisher: American Mathematical Soc.

Published: 1993

Total Pages: 98

ISBN-13: 0821825712

DOWNLOAD EBOOK

The main axiom for a vertex operator algebra (over a field of characteristic zero), the Jacobi identity, is extended to multi-operator identities. Then relative [bold capital]Z2-twisted vertex operators are introduced and a Jacobi identity for these operators is established. Then these ideas are used to interpret and recover the twisted [bold capital]Z-operators and corresponding generating function identities developed by Lepowsky and R. L. Wilson. This work is closely related to the twisted parafermion algebra constructed by Zamolodchikov-Fateev.

On the Correlation of Multiplicative and the Sum of Additive Arithmetic Functions
On the Correlation of Multiplicative and the Sum of Additive Arithmetic Functions

Author: Peter D. T. A. Elliott

Publisher: American Mathematical Soc.

Published: 1994

Total Pages: 102

ISBN-13: 0821825984

DOWNLOAD EBOOK

The correlation of multiplicative arithmetic functions on distinct arithmetic progressions and with values in the complex unit disc, cannot be continually near to its possible maximum unless each function is either very close to or very far from a generalized character. Moreover, under accessible condition the second possibility can be ruled out. As a consequence analogs of the standard limit theorems in probabilistic number theory are obtained with the classical single additive function on the integers replaced by a sum of two additive functions on distinct arithmetic progressions.

Christoffel Functions and Orthogonal Polynomials for Exponential Weights on $[-1, 1]$
Christoffel Functions and Orthogonal Polynomials for Exponential Weights on $[-1, 1]$

Author: A. L. Levin

Publisher: American Mathematical Soc.

Published: 1994

Total Pages: 166

ISBN-13: 0821825992

DOWNLOAD EBOOK

Bounds for orthogonal polynomials which hold on the 'whole' interval of orthogonality are crucial to investigating mean convergence of orthogonal expansions, weighted approximation theory, and the structure of weighted spaces. This book focuses on a method of obtaining such bounds for orthogonal polynomials (and their Christoffel functions) associated with weights on [-1,1]. Also presented are uniform estimates of spacing of zeros of orthogonal polynomials and applications to weighted approximation theory.

On the Coefficients of Cyclotomic Polynomials
On the Coefficients of Cyclotomic Polynomials

Author: Gennady Bachman

Publisher: American Mathematical Soc.

Published: 1993

Total Pages: 93

ISBN-13: 0821825720

DOWNLOAD EBOOK

Let [italic]a([italic]m, [italic]n) denote the [italic]mth coefficient of the [italic]nth cyclotomic polynomial [capital Greek]Phi[subscript italic]n([italic]z), and let [italic]a([italic]m) = max[subscript italic]n [conditional event/restriction/such that] |[italic]a([italic]m, [italic]n)[conditional event/restriction/such that] |. Our principal result is an asymptotic formula for log [italic]a([italic]m) that improves over a recent estimate of Montgomery and Vaughan.