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Field name	Details
Dewey Class	515.2433
Title	Walsh Series and Transforms ([EBook]) : Theory and Applications / by B. Golubov, A. Efimov, V. Skvortsov.
Author	Golubov, Boris Ivanovich
Added Personal Name	Efimov, Aleksej
Added Personal Name	Skvortsov, Valentin Anatolevich
Other name(s)	SpringerLink (Online service)
Publication	Dordrecht : Springer Netherlands , 1991.
Physical Details	XIII, 368 pages : online resource.
Series	Mathematics and its applications. Soviet series 0169-6378 ; ; 64
ISBN	9789401132886
Contents note	1 Walsh Functions and Their Generalizations -- §1.1 The Walsh functions on the interval [0, 1) -- §1.2 The Walsh system on the group -- §1.3 Other definitions of the Walsh system. Its connection with the Haar system -- §1.4 Walsh series. The Dirichlet kernel -- §1.5 Multiplicative systems and their continual analogues -- 2 Walsh-Fourier Series Basic Properties -- §2.1 Elementary properties of Walsh-Fourier series. Formulae for partial sums -- §2.2 The Lebesgue constants -- §2.3 Moduli of continuity of functions and uniform convergence of Walsh-Fourier series -- §2.4 Other tests for uniform convergence -- §2.5 The localization principle. Tests for convergence of a Walsh-Fourier series at a point -- §2.6 The Walsh system as a complete, closed system -- §2.7 Estimates of Walsh-Fourier coefficients. Absolute convergence of Walsh-Fourier series -- §2.8 Fourier series in multiplicative systems -- 3 General Walsh Series and Fourier-Stieltjes Series Questions on Uniqueness of Representation of Functions by Walsh Series -- §3.1 General Walsh series as a generalized Stieltjcs series -- §3.2 Uniqueness theorems for representation of functions by pointwise convergent Walsh series -- §3.3 A localization theorem for general Walsh series -- §3.4 Examples of null series in the Walsh system. The concept of U-sets and M-sets -- 4 Summation of Walsh Series by the Method of Arithmetic Mean -- §4.1 Linear methods of summation. Regularity of the arithmetic means -- §4.2 The kernel for the method of arithmetic means for Walsh- Fourier series -- §4.3 Uniform (C, 1) summability of Walsh-Fourier series of continuous functions -- §4.4 (C, 1) summability of Fourier-Stieltjes series -- 5 Operators in the Theory of Walsh-Fourier Series -- §5.1 Some information from the theory of operators on spaces of measurable functions -- §5.2 The Hardy-Littlewood maximal operator corresponding to sequences of dyadic nets -- §5.3 Partial sums of Walsh-Fourier series as operators -- §5.4 Convergence of Walsh-Fourier series in Lp[0, 1) -- 6 Generalized Multiplicative Transforms -- §6.1 Existence and properties of generalized multiplicative transforms -- §6.2 Representation of functions in L1(0, ?) by their multiplicative transforms -- §6.3 Representation of functions in Lp(0, ?), 1 < p ? 2, by their multiplicative transforms -- 7 Walsh Series with Monotone Decreasing Coefficient -- §7.1 Convergence and integrability -- §7.2 Series with quasiconvex coefficients -- §7.3 Fourier series of functions in Lp -- 8 Lacunary Subsystems of the Walsh System -- §8.1 The Rademacher system -- §8.2 Other lacunary subsystems -- §8.3 The Central Limit Theorem for lacunary Walsh series -- 9 Divergent Walsh-Fourier Series Almost Everywhere Convergence of Walsh-Fourier Series of L2 Functions -- §9.1 Everywhere divergent Walsh-Fourier series -- §9.2 Almost everywhere convergence of Walsh-Fourier series of L2[0, 1) functions -- 10 Approximations by Walsh and Haar Polynomials -- §10.1 Approximation in uniform norm -- §10.2 Approximation in the Lp norm -- §10.3 Connections between best approximations and integrability conditions -- §10.4 Connections between best approximations and integrability conditions (continued) -- §10.5 Best approximations by means of multiplicative and step functions -- 11 Applications of Multiplicative Series and Transforms to Digital Information Processing -- §11.1 Discrete multiplicative transforms -- §11.2 Computation of the discrete multiplicative transform -- §11.3 Applications of discrete multiplicative transforms to information compression -- §11.4 Peculiarities of processing two-dimensional numerical problems with discrete multiplicative transforms -- §11.5 A description of classes of discrete transforms which allow fast algorithms -- 12 Other Applications of Multiplicative Functions and Transforms -- §12.1 Construction of digital filters based on multiplicative transforms -- §12.2 Multiplicative holographic transformations for image processing -- §12.3 Solutions to certain optimization problems -- Appendices -- Appendix 1 Abelian groups -- Appendix 2 Metric spaces. Metric groups -- Appendix 3 Measure spaces -- Appendix 4 Measurable functions. The Lebesgue integral -- Appendix 5 Normed linear spaces. Hilbert spaces -- Commentary -- References.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/978-94-011-3288-6
Links to Related Works	Subject References: Computational Mathematics and Numerical Analysis . Computer mathematics . Fourier Analysis . Mathematics . Microprocessors . Processor Architectures . Authors: author . Efimov, Aleksej . Efimov, Aleksej . Golubov, Boris Ivanovich . Golubov, Boris Ivanovich . Skvortsov, Valentin Anatolevich . Skvortsov, Valentin . Corporate Authors: SpringerLink (Online service) . Series: Mathematics and its applications. Soviet series . Classification: 515.2433 .

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Walsh Series and Transforms: Theory and Applications

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