Topics in classical analysis and applications in honor of Daniel Waterman / editors, Laura De Carli, Kazaros Kazarian, Mario Milman.

Format:

Book

Contributor:

De Carli, Laura, 1962-

Kazarian, Kazaros.

Milman, Mario.

Waterman, Daniel.

Language:

English

Subjects (All):

Mathematical analysis.

Functional analysis.

Fourier series.

Orthogonal polynomials.

Physical Description:

1 online resource (204 p.)

Edition:

1st ed.

Place of Publication:

Hackensack, N.J. : World Scientific, c2008.

Language Note:

English

Summary:

This book covers a wide range of topics, from orthogonal polynomials to wavelets. It contains several high-quality research papers by prominent experts exploring trends in function theory, orthogonal polynomials, Fourier series, approximation theory, theory of wavelets and applications. The book provides an up-to-date presentation of several important topics in Classical and Modern Analysis. The interested reader will also be able to find stimulating open problems and suggestions for future research.

Contents:

Preface; CONTENTS; My Academic Life D. Waterman; REMINISCENCES; RESEARCH; High Indices; Reflexivity and Summability; Harmonic Analysis; Change of Variable; Fourier Series and Generalized Variation; Representation of Functions, Orthogonal Series; Real Analysis; Summability; Survey Papers; PUBLICATIONS; Papers; Books; DOCTORAL STUDENTS; Reminiscences edited by L. Lardy, J. Troutman (with contributions by L. D'Antonio, G. T. Cargo, Ph. T. Church, D. Dezern, G. Gasper, P. Pierce, E. Poletsky, M. Schramm, F. Prus-Wisniowski, P. Schembari); On Concentrating Idempotents, A Survey J. Marshall Ash

1. From Operators on L2 (Z) to Concentration1.1. Definitions; 1.2. Relating classes of operators; 1.3. A surprising connection; 1.4. Results for L2 Concentration; 1.5. Quantitative results for L2 concentration; 2. A Paper 20 Years in the Making; 2.1. The early years; 2.2. On the virtues of procrastination; 3. The Future; 3.1. A segue; 3.2. The L1 concentration question; 3.3. A conjecture about operators; References; Variants of a Selection Principle for Sequences of Regulated and Non-Regulated Functions V. V. Chistyakov, C. Maniscalco, Y. V. Tretyachenko

1. Regulated Functions and Selection Principles2. Main Results; 3. Properties of N(ε, f, T) for Metric Space Valued Functions; 4. Functions with Values in a Metric Space: Proofs; 5. Functions with Values in a Metric Semigroup; 6. Functions with Values in a Re.exive Separable Banach Space; Acknowledgments; References; Local Lp Inequalities for Gegenbauer Polynomials L. De Carli; 1. Introduction; 2. Preliminaries; 2.1. Four useful Lemmas; 3. Most of the Proofs; References; General Monotone Sequences and Convergence of Trigonometric Series M. Dyachenko, S. Tikhonov; 1. Introduction

2. Uniform and Lp-Convergence3. Convergence Almost Everywhere: One-Dimensional Series; 4. Convergence Almost Everywhere: Multiple Series; 5. Concluding Remarks; Acknowledgments; References; Using Integrals of Squares of Certain Real-Valued Special Functionsto Prove that the P ́olya Ξ(z) Function, the Functions Kiz(a), a > 0,and Some Other Entire Functions Having Only Real ZerosG. Gasper; 1. Introduction; 2. Reality of the Zeros of the Functions Kiz(a) When a > 0; 3. Reality of the Zeros of the Functions Ξ(z) and Fa,c(z); Acknowledgment; References

Functions Whose Moments Form a Geometric Progression M. E. H. Ismail, X. Li1. Introduction; 2. Proofs; References; Characterization of Scaling Functions in a Frame MultiresolutionAnalysis in H2GK. S. Kazarian, A. San Antol ́ın; 1. Introduction; 2. Spaces H2G; 2.1. A-invariant sets; 3. Characterization of Scaling Functions of an FMRA in H2G; 3.1. Definitions and Preliminary results; 3.2. Characterization of scaling functions of an H2G -FMRA and other cases; 4. On the Existence of H2G -MRA and H2G -FMRA; References; An Abstract Coifman-Rochberg-Weiss Commutator Theorem J. Martin, M. Milman

1. Introduction

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

ISBN:

9789812834447

9812834443

OCLC:

820944609