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Dyadic Walsh Analysis from 1924 Onwards Walsh Gibbs Butzer Dyadic Differentiation in Science Volume 1 Foundations 1st Edition by Radomir Stankovic, Paul Leo Butzer, Ferenc Schipp, William R Wade, Weiyi Su, Yasushi Endow ISBN 9462391599 9789462391598

Name: Dyadic Walsh Analysis from 1924 Onwards Walsh Gibbs Butzer Dyadic Differentiation in Science Volume 1 Foundations 1st Edition by Radomir Stankovic, Paul Leo Butzer, Ferenc Schipp, William R Wade, Weiyi Su, Yasushi Endow ISBN 9462391599 9789462391598
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Dyadic Walsh Analysis from 1924 Onwards Walsh Gibbs Butzer Dyadic Differentiation in Science Volume 1 Foundations Atlantis Studies in Mathematics for Engineering and Science 12 Stankovic Digital Instant Download

Author(s): Stankovic

Edition: 1st ed. 2015

File Details: DJVU, 8.46 MB

Year: 2016

Language: english

SKU: EB-51186948 Category: Uncategorized Tag: Stankovic

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Dyadic Walsh Analysis from 1924 Onwards Walsh Gibbs Butzer Dyadic Differentiation in Science Volume 1 Foundations 1st Edition by Radomir Stankovic, Paul Leo Butzer, Ferenc Schipp, William R Wade, Weiyi Su, Yasushi Endow – Ebook PDF Instant Download/Delivery: 9462391599 ,9789462391598
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ISBN 10: 9462391599
ISBN 13: 9789462391598
Author: Radomir Stankovic, Paul Leo Butzer, Ferenc Schipp, William R Wade, Weiyi Su, Yasushi Endow

Dyadic (Walsh) analysis emerged as a new research area in applied mathematics and engineering in early seventies within attempts to provide answers to demands from practice related to application of spectral analysis of different classes of signals, including audio, video, sonar, and radar signals. In the meantime, it evolved in a mature mathematical discipline with fundamental results and important features providing basis for various applications. The book will provide fundamentals of the area through reprinting carefully selected earlier publications followed by overview of recent results concerning particular subjects in the area written by experts, most of them being founders of the field, and some of their followers. In this way, this first volume of the two volume book offers a rather complete coverage of the development of dyadic Walsh analysis, and provides a deep insight into its mathematical foundations necessary for consideration of generalizations and applications that are the subject of the second volume. The presented theory is quite sufficient to be a basis for further research in the subject area as well as to be applied in solving certain new problems or improving existing solutions for tasks in the areas which motivated development of the dyadic analysis.

Dyadic Walsh Analysis from 1924 Onwards Walsh Gibbs Butzer Dyadic Differentiation in Science Volume 1 Foundations 1st Edition Table of contents:

1 Early History of Walsh Analysis

1.1 History of the American School of Walsh Analysis

2 My involvement in Walsh and Dyadic Analysis

References

3 The Origins of the Dyadic Derivative due to James Edmund Gibbs

3.1 Definition of the Gibbs Derivative

3.2 Further Development

References

4 Early Contributions from the Aachen School to Dyadic Walsh Analysis with Applications to Dyadic PD

4.1 Butzer-Wagner Dyadic Derivative

4.2 Further Developments

4.3 A Dyadic PDE, the Wave Equation

4.4 Applications to Approximation by Walsh Polynomials and Walsh-Fourier Series

4.5 Later Contributions from Aachen

4.6 Decimal and Dyadic Systems

4.7 Further Suggestions for Studying Our Monograph

Acknowledgment

References

5 Dyadic Derivative, Summation, Approximation *

5.1 Introduction

5.2 Dyadic Derivative

5.2.1 Dyadic derivative of functions of one variable

5.2.2 Dyadic derivative in the multivariable case

5.2.3 Dyadic derivative on the real line

5.2.4 Dyadic derivative on groups

5.3 Summation, Strong summation

5.3.1 (C,1) summability of Walsh–Fourier series

5.3.2 Strong summability

5.3.3 Summability of multivariable Walsh–Fourier series

5.3.4 Dyadic Ces´aro and Copson operators

5.3.5 Multipliers

References

6 How I Started My Research in Walsh and Dyadic Analysis

References

7 My Involvement with the Dyadic Derivative

References

8 Hardy Spaces in the Theory of Dyadic Derivative

8.1 Introduction

8.2 One-dimensional Hardy Spaces

8.3 The One-dimensional Dyadic Derivative

8.4 d-dimensional Hardy Spaces

8.4.1 The Hardy Spaces H p [0,1)d

8.4.2 The Hardy Spaces Hp[0,1)d

8.5 More-dimensional dyadic derivative

8.5.1 Restricted dyadic derivative

8.5.2 Unrestricted dyadic derivative

References

9 Term by Term Dyadic Differentiation of Walsh Series

9.1 Introduction

9.2 The original problem

9.3 Gap series

9.4 Rapidly converging series

9.5 Term-by-term strong dyadic differentiation

References

10 Why I got Interested in Dyadic Differentiation

11 Dyadic Derivative and Walsh-Fourier Transform

11.1 Introduction

11.2 Notations and Definitions

11.3 Lemmas

11.4 Dyadic Differentiation and Integration of Walsh-Fourier Transform

References

12 How I started my research in Walsh and dyadic analysis

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Tags: Radomir Stankovic, Paul Leo Butzer, Ferenc Schipp, William R Wade, Weiyi Su, Yasushi Endow, Dyadic Walsh Analysis