×
Bloom, Walter R.

Absolute convergence of Fourier series on totally disconnected groups. (English) Zbl 0492.43004

Ark. Mat. 20, 101-109 (1982).
Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page
scan of Zbl 0492.43004

Cited in 3 Documents

MSC:

43A25 Fourier and Fourier-Stieltjes transforms on locally compact and other abelian groups
43A70 Analysis on specific locally compact and other abelian groups
43A15 \(L^p\)-spaces and other function spaces on groups, semigroups, etc.

Keywords:

Lipschitz spaces; absolute convergent Fourier series
Cite Review PDF
Full Text: DOI

References:

[1] Benke, George, Smoothness and absolute convergence of Fourier series in compact totally disconnected groups, J. Funct. Anal., 29, 319-327 (1978) · Zbl 0392.43008 · doi:10.1016/0022-1236(78)90034-4
[2] Benke, George, Trigonometric approximation theory in compact totally disconnected groups, Pacific J. Math., 77, 23-32 (1978) · Zbl 0419.43006
[3] Bernstein, Serge, Sur la convergence absolue des séries trigonométriques, C.R. Acad. Sci. Paris, 158, 1661-1663 (1914) · JFM 45.0409.01
[4] Bloom, Walter R., Bernstein’s inequality for locally compact Abelian groups, J. Austral. Math. Soc., 17, 88-101 (1974) · Zbl 0276.43006
[5] Bloom, Walter R., Jackson’s Theorem for locally compact Abelian groups, Bull. Austral. Math. Soc., 10, 59-66 (1974) · Zbl 0268.43004
[6] Bloom, Walter R., Jackson’s Theorem for finite products and homomorphic images of locally compact Abelian groups, Bull. Austral. Math. Soc., 12, 301-309 (1975) · Zbl 0293.43005
[7] Walter R. Bloom, Absolute convergence of Fourier series on finite dimensional groups,Colloq. Math. (to appear). · Zbl 0499.43004
[8] John Scott Bradley,Interpolation theory and Lipschitz classes on totally disconnected groups, M. Sc. Thesis, The University of British Columbia, 1974.
[9] Fine, N. J., On the Walsh functions, Trans. Amer. Math. Soc., 65, 372-414 (1949) · Zbl 0036.03604 · doi:10.2307/1990619
[10] Graham, Colin C., The Sidon constant of a finite abelian group, Proc. Amer. Math. Soc., 68, 83-84 (1978) · Zbl 0377.43006 · doi:10.2307/2040913
[11] Hewitt, Edwin; Ross, Kenneth A., Abstract harmonic analysis (1963), Berlin, Heidelberg, New York: Springer-Verlag, Berlin, Heidelberg, New York · Zbl 0115.10603
[12] Kahane, Jean-Pierre, Séries de Fourier absolument convergentes (1970), Berlin, Heidelberg, New York: Springer-Verlag, Berlin, Heidelberg, New York · Zbl 0195.07602
[13] Onneweer, C. W., Absolute convergence of Fourier series on certain groups, Duke Math. J., 39, 599-609 (1972) · Zbl 0252.43016 · doi:10.1215/S0012-7094-72-03965-8
[14] Onneweer, C. W., Absolute convergence of Fourier series on certain groups, II, Duke Math. J., 41, 679-688 (1974) · Zbl 0294.43009 · doi:10.1215/S0012-7094-74-04172-6
[15] Quek, T. S.; Yap, Leonard Y. H., Absolute convergence of Vilenkin-Fourier series, J. Math. Anal. Appl., 74, 1-14 (1980) · Zbl 0434.43008 · doi:10.1016/0022-247X(80)90110-9
[16] Otto Szász, Über den Konvergenzexponenten der Fourierschen Reihen gewisser Funktionenklassen,S.-B. Bayer. Akad. Wiss. Math.-Phys. Kl. 1922, 135-150. · JFM 48.0304.02
[17] Szász, Otto, Über die Fourierschen Reihen gewisser Funktionenklassen, Math. Ann., 100, 530-536 (1928) · JFM 54.0309.01 · doi:10.1007/BF01448861
[18] Titchmarsh, E. C., A note on Fourier transforms, J. London Math. Soc., 2, 148-150 (1927) · JFM 53.0274.02 · doi:10.1112/jlms/s1-2.3.148
[19] Vilenkin, N. Ja., On a class of complete orthonormal systems, Izv. Akad. Nauk SSSR Ser. Mat., 11, 363-400 (1947) · Zbl 0036.35601
[20] Vilenkin, N. Ya.; Rubinshtein, A. I., A theorem of S. B. Stechkin on absolute convergence of a series with respect to systems of characters on zero-dimensional abelian groups, Izv. Vysš. Učebn. Zaved. Matematika, 19, 3-9 (1975)
[21] Walker, P. L., Lipschitz classes on 0-dimensional groups, Proc. Cambridge Philos. Soc., 63, 923-928 (1967) · Zbl 0184.36301
[22] Walker, P. L., Lipschitz classes on finite dimensional groups, Proc. Cambridge Philos. Soc., 66, 31-38 (1969) · Zbl 0176.44801 · doi:10.1017/S0305004100044686
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.