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Fourier series on the ring of integers in a $p$-series field
Author:
Mitchell H. Taibleson
Journal:
Bull. Amer. Math. Soc. 73 (1967), 623-629
MathSciNet review:
0217522
Full-text PDF
References |
Additional Information
- 1.
N.
J. Fine, On the Walsh functions, Trans. Amer. Math. Soc. 65 (1949), 372–414. MR 0032833
(11,352b), http://dx.doi.org/10.1090/S0002-9947-1949-0032833-2
- 2.
N.
J. Fine, Cesàro summability of Walsh-Fourier series,
Proc. Nat. Acad. Sci. U.S.A. 41 (1955), 588–591. MR 0070757
(17,31f)
- 3.
L.
H. Harper, Capacities of sets and harmonic
analysis on the group 2^{𝜔}, Trans.
Amer. Math. Soc. 126 (1967), 303–315. MR 0206627
(34 #6445), http://dx.doi.org/10.1090/S0002-9947-1967-0206627-X
- 4.
Keith
Phillips, Hilbert transforms for the 𝑝-adic and
𝑝-series fields, Pacific J. Math. 23 (1967),
329–347. MR 0239471
(39 #828)
- 5.
P.
J. Sally Jr. and M.
H. Taibleson, Special functions on locally compact fields,
Acta Math. 116 (1966), 279–309. MR 0206349
(34 #6168)
- 6.
E.
Study, Ueber eine besondere Classe von Functionen einer reellen
Veränderlichen, Math. Ann. 47 (1896),
no. 2-3, 298–316 (German). MR
1510906, http://dx.doi.org/10.1007/BF01447272
- 7.
M. H. Taibleson, Harmonic analysis on n-dimensional vector spaces over local fields, I, Basic results on fractional integration, (to appear).
- 8.
N.
Ja. Vilenkin, On a class of complete orthonormal systems,
Amer. Math. Soc. Transl. (2) 28 (1963), 1–35. MR 0154042
(27 #4001)
- 1.
- N. J. Fine, On the Walsh functions, Trans. Amer. Math. Soc. 65 (1949), 372-414. MR 32833
- 2.
- N. J. Fine, Cesáro sunvmability of Walsh-Fourier series, Proc. Nat. Acad. Sci. U.S.A. 41 (1955), 588-591. MR 70757
- 3.
- L. H. Harper, Capacities of sets and harmonic analysis on the group 2, Trans. Amer. Math. Soc. 126 (1967), 303-315. MR 206627
- 4.
- K. L. Phillips, Hilbert transforms for the p-adic and p-series fields, Pacific J. Math, (to appear). MR 239471
- 5.
- P. J. Sally, Jr. and M. H. Taibleson, Special functions on locally compact fields, Acta Math. 116 (1966), 279-309. MR 206349
- 6.
- E. Study, Ueber eine besondere Classe von Functionen einer reelen Verändlichen, Math. Ann. 47 (1896), 298-316. MR 1510906
- 7.
- M. H. Taibleson, Harmonic analysis on n-dimensional vector spaces over local fields, I, Basic results on fractional integration, (to appear).
- 8.
- N. Ja. Vilenkin, On a class of complete orthonormal systems, Amer. Math. Soc. Transl. (2) 28 (1963), 1-35. MR 154042
Additional Information
DOI:
http://dx.doi.org/10.1090/S0002-9904-1967-11801-9
PII:
S 0002-9904(1967)11801-9
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