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Conjugate Fourier series on certain solenoids. (English) Zbl 0521.43007


MSC:

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

Citations:

Zbl 0448.42005
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Full Text: DOI

References:

[1] Richard Arens and I. M. Singer, Generalized analytic functions, Trans. Amer. Math. Soc. 81 (1956), 379 – 393. · Zbl 0078.10902
[2] Errett Bishop, Representing measures for points in a uniform algebra, Bull. Amer. Math. Soc. 70 (1964), 121 – 122. · Zbl 0196.15202
[3] J. L. Doob, Stochastic processes, John Wiley & Sons, Inc., New York; Chapman & Hall, Limited, London, 1953. · Zbl 0053.26802
[4] John B. Garnett, Bounded analytic functions, Pure and Applied Mathematics, vol. 96, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York-London, 1981. · Zbl 0469.30024
[5] L. L. Helms, Introduction to potential theory, Pure and Applied Mathematics, Vol. XXII, Wiley-Interscience A Division of John Wiley & Sons, New York-London-Sydney, 1969. · Zbl 0188.17203
[6] Henry Helson, Conjugate series in several variables, Pacific J. Math. 9 (1959), 513 – 523. · Zbl 0088.05002
[7] Edwin Hewitt and Gunter Ritter, Fourier series on certain solenoids, Math. Ann. 257 (1981), no. 1, 61 – 83. · Zbl 0448.42005 · doi:10.1007/BF01450655
[8] Edwin Hewitt and Kenneth A. Ross, Abstract harmonic analysis. Vol. I, 2nd ed., Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 115, Springer-Verlag, Berlin-New York, 1979. Structure of topological groups, integration theory, group representations. · Zbl 0416.43001
[9] Edwin Hewitt and Herbert S. Zuckerman, The \?\(_{1}\)-algebra of a commutative semigroup, Trans. Amer. Math. Soc. 83 (1956), 70 – 97. · Zbl 0072.12701
[10] J. Priwaloff, Sur les fonctions conjuguées, Bull. Soc. Math. France 44 (1916), 100 – 103 (French). · JFM 46.0540.03
[11] -, The Cauchy integral, Saratov, U. S. S. R., Publ. Univ., Phys.-Math. Faculty 11:1, 1918.
[12] Marcel Riesz, Sur les fonctions conjuguées, Math. Z. 27 (1928), no. 1, 218 – 244 (French). · JFM 53.0259.02 · doi:10.1007/BF01171098
[13] Walter Rudin, Fourier analysis on groups, Interscience Tracts in Pure and Applied Mathematics, No. 12, Interscience Publishers (a division of John Wiley and Sons), New York-London, 1962. · Zbl 0105.09504
[14] Edgar Lee Stout, The theory of uniform algebras, Bogden & Quigley, Inc., Tarrytown-on-Hudson, N. Y., 1971. · Zbl 0286.46049
[15] E. C. Titchmarsh, Reciprocal formulae involving series and integrals, Math. Z. 25 (1926), no. 1, 321 – 347. · JFM 52.0213.03 · doi:10.1007/BF01283842
[16] -, Introduction to the theory of Fourier integrals, Oxford Univ. Press, Oxford, 1937 (reprinted with corrections, 1967).
[17] Shigeki Yano, Notes on Fourier analysis. XXIX. An extrapolation theorem, J. Math. Soc. Japan 3 (1951), 296 – 305. · Zbl 0045.17901 · doi:10.2969/jmsj/00320296
[18] Antoni Zygmund, Sur les fonctions conjuguées, Fund. Math. 13 (1929), 284-303; Corrigenda, ibid. 18 (1932), 312.
[19] -, Trigonometric series, Vol. I, 2nd ed., Cambridge Univ. Press, Cambridge, 1959 (reprinted with corrections and additions, 1968 and 1977).
[20] -, Trigonometric series, Vol. II, 2nd ed., Same bibliography as item [19]. · Zbl 0072.28503
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