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Pseudo functions and uniqueness on the group of integers of a p-series field. (English) Zbl 0438.43008


MSC:

43A50 Convergence of Fourier series and of inverse transforms
43A46 Special sets (thin sets, Kronecker sets, Helson sets, Ditkin sets, Sidon sets, etc.)

Citations:

Zbl 0402.43006
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References:

[1] G. Agaev, A Weiner type theorem for series of Walsh functions,Dokl. Akad. Nauk SSSR’ 142 (1962), 751–753.
[2] N. Dunford andJ. T. Schwartz,Linear Operators, I and II, Interscience Publishers, (New York, 1958). · Zbl 0084.10402
[3] N. J. Fine, On the Walsh functions,Trans. A.M.S.,65 (1949), 372–414. · Zbl 0036.03604 · doi:10.1090/S0002-9947-1949-0032833-2
[4] J. E. Giles,Sets of uniqueness for Walsh functions, Doctoral Dissertation, University of Tennessee (1974).
[5] I. I. Pyateskiį-Shapiro, Supplement to the work, ”On the problem of uniqueness of expansions of a function in a trigonometric series”Uchen. Zapiski Mosk., Univer.,165, 7 (1954), 78–97.
[6] M. H. Taibleson, Fourier Analysis on Local Fields,Mathematical Notes, Princeton University Press (Princeton, 1975). · Zbl 0319.42011
[7] N. Ja. Vilenkin, On a class of complete orthonormal systems,Izv. Akad. Nauk SSSR. 11 (1947), 363–400.
[8] W. R. Wade, Sets of uniqueness for the group of integers of ap-series field,Can. J. Math.,31 (1979), 858–866. · Zbl 0415.43013 · doi:10.4153/CJM-1979-081-7
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