Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
|
   
Available in electronic format
Available in print format 		Bulletin of the American Mathematical Society
Bulletin of the American Mathematical Society
ISSN 1088-9485(e) ISSN 0273-0979(p)

     

Book Review

The AMS does not provide abstracts of book reviews. You may download the entire review from the links below.

Retrieve article in: PDF

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. Rubinshteĭn, Multiplicative systems and harmonic analysis on zero-dimensional groups, Baku "ELM," 1981.

[2]
G. Alexits, Sur la sommabilité des séries orthogonales, Acta Math. Acad. Sci. Hungar. 4 (1953), 181-188. MR 0061193 (15:788i)

[3]
F. G. Arutunyan and A. A. Talalyan, On uniqueness of Haar and Walsh series, Izv. Akad. Nauk SSSR 28 (1964), 1391-1408. MR 0172056 (30:2282)

[4]
B. Aubertin, Algebraic elements and sets of uniqueness in the group integers of a p-series field, Canad. Math. Bull.. 29 (1986), 177-184. MR 844896 (87j:43011)

[5]
L. A. Balashov and A. I. Rubinshteĭn, Series with respect to the Walsh system and their generalizations, J. Soviet Math. 1 (1973), 727-763.

[6]
L. A. Balashov and V. A. Skvortsov, Gibbs phenomenon for the Walsh system, Dokl. Akad. Nauk SSSR 268 (1983), 1033-1034. MR 697817 (84e:42027)

[7]
K. G. Beauchamp, Walsh functions and their applications, Academic Press, New York, 1975. MR 0462758 (57:2731)

[8]
A. D. Bethke, Genetic algorithms as function optimizers, Dissertation, Univ. of Michigan, 1980.

[9]
S. V. Bochkarev, The Walsh Fourier coefficients, Izv. Akad. SSSR, Ser. Mat. 34 (1970), 203-208. MR 0259474 (41:4112)

[10]
D. L. Burkholder, Martingale transforms, Ann. Math. Stat. 37 (1966), 1494-1504. MR 0208647 (34:8456)

[11]
P. L. Butzer and H. J. Wagner, Walsh series and the concept of a derivative, Applicable Anal. 3 (1973), 29-46. MR 0404978 (53:8774)

[12]
R. R. Coifman and R. S. Strichartz, The school of Antoni Zygmund, A Century of Mathematics in America, part III, Amer. Math. Soc., Providence, RI, 1989, pp. 343-368. MR 1025352 (91h:01091)

[13]
R. R. Coifman and G. Weiss, Extensions of Hardy spaces and their use in analysis, Bull. Amer. Math. Soc. 83 (1977), 569-645. MR 0447954 (56:6264)

[14]
R. B. Crittenden and V. L. Shapiro, Sets of uniqueness on the group $ {2^\omega }$, Ann. of Math. (2) 81 (1965), 550-564. MR 0179535 (31:3783)

[15]
P. Enflo, A counterexample to the approximation property in Banach spaces, Acta Math. 139 (1973), 308-317. MR 0402468 (53:6288)

[16]
W. Engels, On the characterization of the dyadic derivative, Acta Math. Acad. Sci. Hungar. 46 (1985), 47-56. MR 819052 (87a:42042)

[17]
C. Fefferman and E. M. Stein, $ {H^P}$ spaces of several variables, Acta Math. 129 (1972), 137-194. MR 0447953 (56:6263)

[18]
N. J. Fine, On the Walsh functions, Trans. Amer. Math. Soc. 65 (1949), 372-414. MR 0032833 (11:352b)

[19]
-, The generalized Walsh functions, Trans. Amer. Math. Soc. 69 (1950), 66-77. MR 0042535 (13:126g)

[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. 45 (1985), 223-234. MR 779509 (86m:42032)

[21]
J. B. Garnett and P. W. Jones, BMO and dyadic BMO, Pacific J. Math. 99 (1982), 351-371. MR 658065 (85d:42021)

[22]
A. M. Garsia, Martingale inequalities, W. A. Benjamin, Inc., Reading, MA, 1973. MR 0448538 (56:6844)

[23]
J. E. Gibbs and M. S. Millard, Walsh functions as solutions of a logical differential equation, National Physical Lab. 1969, Middlesex, England, DES Report No. 1.

[24]
D. J. Grubb, Sets of uniqueness in compact, 0-dimensional metric groups, Trans. Amer. Math. Soc. 301 (1987), 239-249. MR 879571 (88h:42029)

[25]
-, Summation methods and uniqueness in Vilenkin groups, Proc. Amer. Math. Soc. 102 (1988), 556-558. MR 928979 (89b:42019)

[26]
R. F. Gundy, Martingale theory and pointwise convergence of certain orthogonal series, Trans. Amer. Math. Soc. 124 (1966), 228-248. MR 0204967 (34:4802)

[27]
A. Haar, Zur theorie der orthogonalen funktionen systems, Mat. Ann. 69 (1910), 331-371. MR 1511592

[28]
H. F. Harmuth, Sequency theory, Academic Press, New York, 1977. MR 0434596 (55:7561)

[29]
-, Transmission of information by orthogonal functions, Springer-Verlag, Berlin, 1972. MR 0347427 (49:12147)

[30]
D. Harris, Compact sets of divergence for continuous functions on a Vilenkin group, Proc. Amer. Math. Soc. 98 (1986), 436-440. MR 857936 (87m:43006)

[31]
R. A. Hunt, Almost everywhere convergence of Walsh-Fourier series of $ {L^2}$ functions, Actes Congres. Internat. Math. 2 (1970), 655-661. MR 0511000 (58:23330)

[32]
S. V. Konyagin, Limits of indeterminacy of trigonometric series, Math. Notes, no. 44, Princeton Univ. Press, Princeton, NJ, pp. 910-919. MR 983549 (90g:42012)

[33]
N. R. Ladhawala, Absolute summability of Walsh-Fourier series, Pacific J. Math. 65 (1976), 103-108. MR 0417678 (54:5727)

[34]
S. V. Levizov, Some properties of the Walsh system, Mat. Z. 27 (1980), 715-720. MR 578256 (81g:42028)

[35]
M. Maqusi, Applied Walsh analysis, Heyden, London, 1981. MR 825742 (87c:42027)

[36]
K. H. Moon, An everywhere divergent Fourier-Walsh series of the class $ L{({\log ^ + }{\log ^ + }L)^{1 - \varepsilon }}$, Proc. Amer. Math. Soc. 50 (1975), 309-314. MR 0377406 (51:13578)

[37]
G. W. Morgenthaler, Walsh-Fourier series, Trans. Amer. Math. Soc. 84 (1957), 472-507. MR 0091370 (19:956d)

[38]
C. W. Onneweer, On uniform convergence of Walsh-Fourier series, Pacific J. Math. 34 (1970), 117-122. MR 0275048 (43:806)

[39]
C. W. Onneweer and D. Waterman, Fourier series of functions of harmonic bounded fluctuation, J. d'Anal. Math. 27 (1974), 79-93. MR 0481938 (58:2029)

[40]
R. E. A. C. Paley, A remarkable system of orthogonal functions, Proc. London Math. Soc. 34 (1932), 241-279.

[41]
J. J. Price, Orthonormal sets with non-negative Dirichlet kernels, II, Trans. Amer. Math. Soc. 100 (1961), 153-161. MR 0126124 (23:A3420)

[42]
W. Rudin, Fourier analysis on groups, Interscience, Wiley and Sons, New York and London, 1967. MR 1038803 (91b:43002)

[43]
F. Schipp, Pointwise convergence of expansions with respect to certain product systems, Anal. Math. 2 (1976), 65-76. MR 0415190 (54:3281)

[44]
-, Über die divergenz der Walsh-Fourier reihen, Ann. Univ. Sci. Budapest. Eötvös Sect. Math. 12 (1969), 49-62. MR 0256054 (41:714)

[45]
F. Schipp, W. R. Wade, and P. Simon, Walsh series: an introduction to dyadic harmonic analysis, Adam Hilger, Ltd., Bristol and New York, 1990. MR 1117682 (92g:42001)

[46]
A. A. Schneĭder, Uniqueness of expansions with respect to the Walsh system of functions, Mat. Sb. 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 Eötvös Sect. Math. 27 (1984), 87-101. MR 823096 (87b:42032)

[49]
P. Sjölin, An inequality of Paley and convergence a.e. of Walsh-Fourier series, Ark. Mat. (1969), 551-570. MR 0241885 (39:3222)

[50]
V A. Skvortsov, Differentiation with respect to nets and the Haar series, Mat. Z. 4 (1968), 33-40. MR 0236606 (38:4901)

[51]
-, Some generalizations of the uniqueness theorem for Walsh series, Mat. Z. 13 (1973), 367-372. MR 0318767 (47:7313)

[52]
V. A. Skvortsov and W. R. Wade, Generalizations of some results concerning Walsh series and the dyadic derivative, Anal. Math. 5 (1979), 249-255. MR 549241 (80i:42017)

[53]
R. S. Stanković and J. E. Gibbs, Bibliography of Gibbs derivatives, Theory and Applications of Gibbs Derivatives, Institute of Mathematics, Belgrade, 1989, pp. XV-XXIV.

[54]
M. H. Taibleson, Fourier analysis on local fields, Princeton Univ. Press, Princeton, NJ, 1975. MR 0487295 (58:6943)

[55]
A. A. Talalyan and F. G. Arutunyan, Convergence of series with respect to the Haar system to $ + \infty $, Mat. Sb. 66 (1965), 240-247.

[56]
N. Y. Vilenkin, A class of complete orthonormal series, Izv. Akad. Nauk SSSR Ser. Mat. 11 (1947), 363-400. MR 0022560 (9:224h)

[57]
I. V. Volovich, p-adic string, classical and quantum gravity, Teor. Mat. Fiz. 71 (1987). MR 895889 (88h:81217)

[58]
W. R. Wade, Recent developments in the theory of Walsh series, Internat. J. Math. 5 (1982), 625-673. MR 679409 (84d:42033)

[59]
-, Vilenkin-Fourier series and approximation, Colloq. Math. Soc. J. Bolyai (to appear).

[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. 84 (1982), 202-206. MR 637169 (83c:43010)

[61]
J. L. Walsh, A closed set of normal orthogonal functions, Amer. J. Math. 45 (1923), 5-24. MR 1506485

[62]
D. Waterman, On systems of functions resembling the Walsh system, Michigan Math. J. 29 (1982), 83-87. MR 646374 (85a:42039)

[63]
Sh. Yano, On Walsh series, Tôhoku Math. J. 3 (1951), 223-242. MR 0045236 (13:550a)

[64]
-, Cesàro summability of Walsh-Fourier series, Tôhoku Math. J. 9 (1957), 267-272. MR 0095384 (20:1887)

[65]
K. Yoneda, Perfect sets of uniqueness on the group $ {2^\omega }$, Canad. J. Math. 34 (1982), 759-764. MR 663317 (83h:42030)

[66]
Wo-Sang Young, A note on Walsh-Fourier series, Proc. Amer. Math. Soc. 59 (1976), 305-310. MR 0410247 (53:13997)

[67]
L. A. Zalmanzon, Fourier, Walsh, and Haar transforms, Moskva "Nauka", 1989. MR 1044560 (91i:94001)

[68]
A. Zygmund, Trigonometric series, Cambridge Univ. Press, New York, 1959. MR 0107776 (21:6498)

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




AMS and Social Media LinkedIn Facebook Podcasts Twitter YouTube RSS Feeds Blogs Wikipedia