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Book Information
Author(s):
Golubov, Efimov, and Skvortsov
Title:
Walsh series and transforms
Additional book information:
Kluwer Academic Publishers, Dordrecht, The Netherlands 1991, 367 pp., US$169.00. ISBN 0-7923-1100-0
References:
- [1]
- G. N. Agaev, N. Ya. Vilenkin, G. M. Dzafarli, and A. I. Rubinshte\u \i n, Multiplicative systems and harmonic analysis on zero-dimensional groups, Baku ``ELM,'' 1981.
- [2]
- G. Alexits, Sur la sommabilit\'e des s\'eries orthogonales, Acta Math. Acad. Sci. Hungar. \textbf{4} (1953), 181--188.
- [3]
- F. G. Arutunyan and A. A. Talalyan, On uniqueness of Haar and Walsh series, Izv. Akad. Nauk SSSR \textbf{28} (1964), 1391--1408.
- [4]
- B. Aubertin, Algebraic elements and sets of uniqueness in the group integers of a $p$-series field, Canad. Math. Bull. \textbf{29} (1986), 177--184.
- [5]
- L. A. Balashov and A. I. Rubinshte\u \i n, Series with respect to the Walsh system and their generalizations, J. Soviet Math. \textbf{1} (1973), 727--763.
- [6]
- L. A. Balashov and V. A. Skvortsov, Gibbs phenomenon for the Walsh system, Dokl. Akad. Nauk SSSR \textbf{268} (1983), 1033--1034.
- [7]
- K. G. Beauchamp, Walsh functions and their applications, Academic Press, New York, 1975.
- [8]
- A. D. Bethke, \emph{Genetic algorithms as function optimizers}, 1980.
- [9]
- S. V. Bochkarev, The Walsh Fourier coefficients, Izv. Akad. SSSR, Ser. Mat. \textbf{34} (1970), 203--208.
- [10]
- D. L. Burkholder, Martingale transforms, Ann. Math. Stat. \textbf{37} (1966), 1494--1504.
- [11]
- P. L. Butzer and H. J. Wagner, Walsh series and the concept of a derivative, Applicable Anal. \textbf{3} (1973), 29--46.
- [12]
- R. R. Coifman and R. S. Strichartz, \emph{The school of Antoni Zygmund}, Amer. Math. Soc., Providence, RI, 1989 pp.~343--368.
- [13]
- R. R. Coifman and G. Weiss, Extensions of Hardy spaces and their use in analysis, Bull. Amer. Math. Soc. \textbf{83} (1977), 569--645.
- [14]
- R. B. Crittenden and V. L. Shapiro, Sets of uniqueness on the group $2^\omega $, Ann. of Math. (2) \textbf{81} (1965), 550--564.
- [15]
- P. Enflo, A counterexample to the approximation property in Banach spaces, Acta Math. \textbf{139} (1973), 308--317.
- [16]
- W. Engels, On the characterization of the dyadic derivative, Acta Math. Acad. Sci. Hungar. \textbf{46} (1985), 47--56.
- [17]
- C. Fefferman and E. M. Stein, $H^p$ spaces of several variables, Acta Math. \textbf{129} (1972), 137--194.
- [18]
- N. J. Fine, On the Walsh functions, Trans. Amer. Math. Soc. \textbf{65} (1949), 372--414.
- [19]
- N. J. Fine, The generalized Walsh functions, Trans. Amer. Math. Soc. \textbf{69} (1950), 66--77.
- [20]
- S. Fridli and P. Simon, On the Dirichlet kernels and a Hardy space with respect to the Vilenkin system, Acta Math. Acad. Sci. Hungar. \textbf{45} (1985), 223--234.
- [21]
- J. B. Garnett and P. W. Jones, BMO and dyadic BMO, Pacific J. Math. \textbf{99} (1982), 351--371.
- [22]
- A. M. Garsia, Martingale inequalities, W. A. Benjamin, Inc., Reading, MA, 1973.
- [23]
- J. E. Gibbs and M. S. Millard, \emph{Walsh functions as solutions of a logical differential equation}.
- [24]
- D. J. Grubb, Sets of uniqueness in compact, $0$-dimensional metric groups, Trans. Amer. Math. Soc. \textbf{301} (1987), 239--249.
- [25]
- D. J. Grubb, Summation methods and uniqueness in Vilenkin groups, Proc. Amer. Math. Soc. \textbf{102} (1988), 556--558.
- [26]
- R. F. Gundy, Martingale theory and pointwise convergence of certain orthogonal series, Trans. Amer. Math. Soc. \textbf{124} (1966), 228--248.
- [27]
- A. Haar, Zur theorie der orthogonalen funktionen systems, Mat. Ann. \textbf{69} (1910), 331--371.
- [28]
- H. F. Harmuth, Sequency theory, Academic Press, New York, 1977.
- [29]
- H. F. Harmuth, Transmission of information by orthogonal functions, Springer-Verlag, Berlin, 1972.
- [30]
- D. Harris, Compact sets of divergence for continuous functions on a Vilenkin group, Proc. Amer. Math. Soc. \textbf{98} (1986), 436--440.
- [31]
- R. A. Hunt, Almost everywhere convergence of Walsh-Fourier series of $L^2$ functions, Actes Congres. Internat. Math. \textbf{2} (1970), 655--661.
- [32]
- S. V. Konyagin, \emph{Limits of indeterminacy of trigonometric series}, Princeton Univ. Press, Princeton, NJ pp.~910--919.
- [33]
- N. R. Ladhawala, Absolute summability of Walsh-Fourier series, Pacific J. Math. \textbf{65} (1976), 103--108.
- [34]
- S. V. Levizov, Some properties of the Walsh system, Mat. Z. \textbf{27} (1980), 715--720.
- [35]
- M. Maqusi, Applied Walsh analysis, Heyden, London, 1981.
- [36]
- K. H. Moon, An everywhere divergent Fourier-Walsh series of the class $L(\operatorname {log}^+\operatorname {log}^+ L)^{1-\varepsilon }$, Proc. Amer. Math. Soc. \textbf{50} (1975), 309--314.
- [37]
- G. W. Morgenthaler, Walsh-Fourier series, Trans. Amer. Math. Soc. \textbf{84} (1957), 472--507.
- [38]
- C. W. Onneweer, On uniform convergence of Walsh-Fourier series, Pacific J. Math. \textbf{34} (1970), 117--122.
- [39]
- C. W. Onneweer and D. Waterman, Fourier series of functions of harmonic bounded fluctuation, J. d'Anal. Math. \textbf{27} (1974), 79--93.
- [40]
- R. E. A. C. Paley, A remarkable system of orthogonal functions, Proc. London Math. Soc. \textbf{34} (1932), 241--279.
- [41]
- J. J. Price, Orthonormal sets with non-negative Dirichlet kernels {\rm II}, Trans. Amer. Math. Soc. \textbf{100} (1961), 153--161.
- [42]
- W. Rudin, Fourier analysis on groups, Interscience, Wiley and Sons, New York and London, 1967.
- [43]
- F. Schipp, Pointwise convergence of expansions with respect to certain product systems, Anal. Math. \textbf{2} (1976), 65--76.
- [44]
- F. Schipp, \"Uber die divergenz der Walsh-Fourier reihen, Ann. Univ. Sci. Budapest. E\"otv\"os Sect. Math. \textbf{12} (1969), 49--62.
- [45]
- F. Schipp, W. R. Wade, and P. Simon, Walsh series\,{\rm :} an introduction to dyadic harmonic analysis, Adam Hilger, Ltd., Bristol and New York, 1990.
- [46]
- A. A. Schne\u \i der, Uniqueness of expansions with respect to the Walsh system of functions, Mat. Sb. \textbf{24} (1949), 279--300.
- [47]
- A. H. Siddiqi, Walsh functions, Aligarh Muslim Univ. Press, Aligarh, India, 1977.
- [48]
- P. Simon, Investigations with respect to the Vilenkin system, Ann. Univ. Sci. Budapest E\"otv\"os Sect. Math. \textbf{27} (1984), 87--101.
- [49]
- P. Sj\"olin, An inequality of Paley and convergence a.e. of Walsh-Fourier series, Ark. Mat. (1969), 551--570.
- [50]
- V A. Skvortsov, Differentiation with respect to nets and the Haar series, Mat. Z. \textbf{4} (1968), 33--40.
- [51]
- V A. Skvortsov, Some generalizations of the uniqueness theorem for Walsh series, Mat. Z. \textbf{13} (1973), 367--372.
- [52]
- V. A. Skvortsov and W. R. Wade, Generalizations of some results concerning Walsh series and the dyadic derivative, Anal. Math. \textbf{5} (1979), 249--255.
- [53]
- R. S. Stankovi\'c and J. E. Gibbs, \emph{Bibliography of Gibbs derivatives} pp.~XV--XXIV.
- [54]
- M. H. Taibleson, Fourier analysis on local fields, Princeton Univ. Press, Princeton, NJ, 1975.
- [55]
- A. A. Talalyan and F. G. Arutunyan, Convergence of series with respect to the Haar system to $+\infty $, Mat. Sb. \textbf{66} (1965), 240--247.
- [56]
- N. Y. Vilenkin, A class of complete orthonormal series, Izv. Akad. Nauk SSSR Ser. Mat. \textbf{11} (1947), 363--400.
- [57]
- I. V. Volovich, $p$-adic string, classical and quantum gravity, Teor. Mat. Fiz. \textbf{71} (1987).
- [58]
- W. R. Wade, Recent developments in the theory of Walsh series, Internat. J. Math. \textbf{5} (1982), 625--673.
- [59]
- W. R. Wade, Vilenkin-Fourier series and approximation, Colloq. Math. Soc. J. Bolyai.
- [60]
- W. R. Wade and K. Yoneda, Uniqueness and quasi-measures on the group of integers of a $p$-series field, Proc. Amer. Math. Soc. \textbf{84} (1982), 202--206.
- [61]
- J. L. Walsh, A closed set of normal orthogonal functions, Amer. J. Math. \textbf{45} (1923), 5--24.
- [62]
- D. Waterman, On systems of functions resembling the Walsh system, Michigan Math. J. \textbf{29} (1982), 83--87.
- [63]
- Sh. Yano, On Walsh series, T\^ohoku Math. J. \textbf{3} (1951), 223--242.
- [64]
- Sh. Yano, Ces\`aro summability of Walsh-Fourier series, T\^ohoku Math. J. \textbf{9} (1957), 267--272.
- [65]
- K. Yoneda, Perfect sets of uniqueness on the group $2^\omega $, Canad. J. Math. \textbf{34} (1982), 759--764.
- [66]
- Wo-Sang Young, A note on Walsh-Fourier series, Proc. Amer. Math. Soc. \textbf{59} (1976), 305--310.
- [67]
- L. A. Zalmanzon, Fourier, Walsh, and Haar transforms, Moskva ``Nauka'', 1989.
- [68]
- A. Zygmund, Trigonometric series, Cambridge Univ. Press, New York, 1959.
Additional Information:
Reviewer(s):
W. R.
Wade
Review Information:
Journal:
Bull. Amer. Math. Soc.
26
(1992),
348-359.
DOI:
10.1090/S0273-0979-1992-00276-8
PII:
S 0273-0979(1992)00276-8
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