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Dyadic Walsh Analysis from 1924 Onwards Walsh-Gibbs-Butzer Dyadic Differentiation in Science Volume 2 Extensions and Generalizations: A Monograph Based on Articles of the Founding Authors, Reproduced in Full 1st ed. 2015 [Kõva köide]

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  • Formaat: Hardback, 360 pages, kõrgus x laius: 235x155 mm, kaal: 6919 g, 9 Illustrations, black and white; XVIII, 360 p. 9 illus., 1 Hardback
  • Sari: Atlantis Studies in Mathematics for Engineering and Science 13
  • Ilmumisaeg: 08-Jan-2016
  • Kirjastus: Atlantis Press (Zeger Karssen)
  • ISBN-10: 9462391629
  • ISBN-13: 9789462391628
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Dyadic Walsh Analysis from 1924 Onwards Walsh-Gibbs-Butzer Dyadic Differentiation in Science Volume 2 Extensions and Generalizations: A Monograph Based on Articles of the Founding Authors, Reproduced in Full 1st ed. 2015Suurem pilt
  • Formaat: Hardback, 360 pages, kõrgus x laius: 235x155 mm, kaal: 6919 g, 9 Illustrations, black and white; XVIII, 360 p. 9 illus., 1 Hardback
  • Sari: Atlantis Studies in Mathematics for Engineering and Science 13
  • Ilmumisaeg: 08-Jan-2016
  • Kirjastus: Atlantis Press (Zeger Karssen)
  • ISBN-10: 9462391629
  • ISBN-13: 9789462391628
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9789462391628.html
Märksõnad:
The second volume of the two volumes book is dedicated to various extensions and generalizations of Dyadic (Walsh) analysis and related applications. Considered are dyadic derivatives on Vilenkin groups and various other Abelian and finite non-Abelian groups. Since some important results were developed in former Soviet Union and China, we provide overviews of former work in these countries. Further, we present translations of three papers that were initially published in Chinese. The presentation continues with chapters written by experts in the area presenting discussions of applications of these results in specific tasks in the area of signal processing and system theory. 

Efficient computing of related differential operators on contemporary hardware, including graphics processing units, is also considered, which makes the methods and techniques of dyadic analysis and generalizations computationally feasible.

The volume 2 of the book ends with a chapter presenting open problems pointed out by several experts in the area.
1 Early Work in Gibbs Differentiation in China
1(64)
Weiyi Su
1.1 Research in Butzer-Gibbs Calculus in China - A glance of p-type calculus
2(3)
References
3(2)
1.2 The Generalized Logical Derivative and Its Applications
5(10)
1.2.1 Introduction
5(2)
1.2.2 The p-adic Logical Derivatives
7(4)
1.2.3 Bernstein Type Inequality and Bernstein Type Theorem
11(3)
References
14(1)
1.3 The Generalized Walsh Transform and An Extremum Problem
15(18)
1.3.1 Introduction
15(1)
1.3.2 Properties of WN-type functions
16(2)
1.3.3 The Descent Order of WN-type Functions
18(5)
1.3.4 p-adic Logic Derivatives
23(1)
1.3.5 Logic derivative
24(1)
1.3.6 Adjoint logic derivative
25(2)
1.3.7 A Class of Extremum Problems
27(5)
References
32(1)
1.4 The Logical Derivatives and Integrals-Zheng Weixing, Su Weiyi
33(16)
1.4.1 Introduction
33(1)
1.4.2 Notation and important results
34(2)
1.4.3 p-adic derivatives and integrals of functions in LqG, 1 ≤ q ≤ 2
36(12)
References
48(1)
1.5 The Logical Derivatives and Integrals Second Part
49(16)
2 Gibbs-Butzer Calculus and Pseudo-differential Operators on Local Fields
65(28)
Weiyi Su
Qiu Hua
2.1 Introduction
65(1)
2.2 Notations
66(1)
2.3 G-B type derivative and G-B type integrals
67(8)
2.4 Function Spaces on Local Fields
75(4)
2.5 A Comparison of Newton calculus with G-B calculus
79(3)
2.6 Applications of Gibbs-Butzer-type Calculus
82(11)
2.6.1 Application to Approximation Theory on Local Fields
82(1)
2.6.2 Application to determine function space for which a function belongs to it
83(1)
2.6.3 Application to partial differential equations with fractal boundaries
84(5)
2.6.4 Application to medical science
89(1)
References
90(3)
3 Early Work in Dyadic Differentiation in Soviet Union - SSSR
93(32)
Radomir S. Stankovic
Paul L. Butzer
3.1 Interest in Dyadic Differentiation in Soviet Union
93(32)
4 Research in Dyadic Differentiation in Russia
125(6)
Boris I. Golubov
Sergei S. Volosivets
References
128(3)
5 Generalized Derivatives and Integrals on Vilenkin Groups
131(14)
Boris I. Golubov
Sergei S. Volosivets
5.1 A. The case of compact groups
131(6)
5.2 B. The case of locally compact groups
137(8)
References
141(4)
6 Calculus on Walsh and Vilenkin Groups
145(12)
Gyorgy Gat
Rodolfo Toledo
6.1 Introduction
145(3)
6.2 Results related to Vilenkin systems
148(3)
6.3 Results related to representative product systems
151(1)
6.4 Results related to Walsh-Kaczmarz systems
152(1)
6.5 Results related to two-dimensional Walsh-Paley systems
153(4)
References
155(2)
7 Gibbs Derivatives on Groups
157(12)
Radomir S. Stankovic
7.1 Introduction
157(2)
7.2 Basic Concepts
159(2)
7.3 Gibbs Derivatives on Finite Non-Abelian Groups
161(4)
7.4 Summary and Recent Work
165(4)
References
166(3)
8 My Research in Gibbs Derivatives on Finite Groups
169(42)
Radomir S. Stankovic
References
171(40)
9 Efficient Computation of Gibbs Derivatives on Finite Abelian Groups
211(66)
Radomir S. Stankovic
Dusan Gajic
9.1 Introduction
211(1)
9.2 Definitions of Gibbs Derivatives on Finite Abelian Groups
212(2)
9.3 Generalizations
214(1)
9.4 Fast Fourier Transform on Finite Abelian Groups
215(2)
9.5 Gibbs Derivatives on Finite Abelian Groups
217(2)
9.6 Computing the Gibbs Derivatives on Finite Abelian Groups
219(1)
9.6.1 Convolution-like algorithm
219(1)
9.6.2 Computing in terms of partial Gibbs derivatives
219(1)
9.7 GPGPU Computing Platform
220(2)
9.8 Mapping the Algorithms to GPGPU Architecture
222(1)
9.9 Experimental Results
223(54)
References
227(50)
10 Gibbs Derivative and Walsh Harmonizable DSP
277(20)
Yasushi Endow
10.1 Introduction
277(1)
10.2 Q-loop and dyadic time
277(2)
10.3 Gibbs derivative and Walsh functions
279(2)
10.3.1 Walsh functions
279(1)
10.3.2 Gibbs derivative
280(1)
10.4 Dyadic system and dyadic flow
281(1)
10.5 Dyadic stationary process
282(4)
10.5.1 DSP in strict sense
282(1)
10.5.2 DSP in wide sense and its W-harmonizability
283(1)
10.5.3 Walsh harmonizability of DSP
284(1)
10.5.4 DSP and LDP
285(1)
10.5.5 Walsh Series and Approximation of DSP
286(1)
10.6 Gibbs Differentiation of DSP
286(2)
10.6.1 Gibbs Differentiability Conditions
287(1)
10.6.2 A Linear Gibbs Differential Equation
287(1)
10.7 Extensions and Comments
288(9)
10.7.1 Chrestenson functions
289(3)
10.7.2 A p-adic SP and C-harmonaizability
292(1)
10.7.3 W-Harmonizable and C-Harmonizable DSPs
293(1)
10.7.4 Open Problems
293(1)
References
294(3)
11 My Involvement in Gibbs Derivatives and Walsh Harmonizable Processes
297(28)
Yasushi Endow
11.0.1 Introduction
297(1)
11.0.2 Walsh Harmonizable DSP
298(1)
11.0.3 DSP and LDP
298(1)
11.0.4 Walsh Series and Approximation of DSP
299(1)
11.0.5 Gibbs Differentiability of DSP
300(1)
11.0.6 A Linear Gibbs Differential Equation
301(1)
11.0.7 Extensions and Comments
302(1)
References
302(23)
12 Open Problems in Theory and Applications of Dyadic Derivatives
325(8)
References
326(1)
References
327(1)
References
328(1)
12.1 Hardy Spaces
329(1)
12.2 The one-dimensional dyadic derivative
330(3)
References
332(1)
List of Publications on Dyadic Differentiation by the Authors of the Book 333(14)
Index 347(4)
Biographies of Authors 351