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Fourier transforms of unbounded measures. (English) Zbl 0214.13003


MSC:

43A05 Measures on groups and semigroups, etc.
43A25 Fourier and Fourier-Stieltjes transforms on locally compact and other abelian groups
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[1] N. Bourbaki, Livre VI: Intégration. Chaps. 1, 8, Actualités Sci. Indust., nos. 1175, 1306, Hermann, Paris, 1965, 1963. MR 31 #3539; MR 36 #2763.
[2] N. Bourbaki, Éléments de mathématique. Fasc. XXXII. Théories spectrales. Chapitre I: Algèbres normées. Chapitre II: Groupes localement compacts commutatifs, Actualités Scientifiques et Industrielles, No. 1332, Hermann, Paris, 1967 (French). · Zbl 0152.32603
[3] Salomon Bochner, Lectures on Fourier integrals. With an author’s supplement on monotonic functions, Stieltjes integrals, and harmonic analysis, Translated by Morris Tenenbaum and Harry Pollard. Annals of Mathematics Studies, No. 42, Princeton University Press, Princeton, N.J., 1959. · Zbl 0085.31802
[4] Edwin Hewitt and Kenneth A. Ross, Abstract harmonic analysis. Vol. I: Structure of topological groups. Integration theory, group representations, Die Grundlehren der mathematischen Wissenschaften, Bd. 115, Academic Press, Inc., Publishers, New York; Springer-Verlag, Berlin-Göttingen-Heidelberg, 1963. · Zbl 0416.43001
[5] J. Glimm, Lectures on harmonic analysis, Courant Institute Notes, New York University, New York, 1965.
[6] Roger Godement, Introduction aux travaux de A. Selberg, Séminaire Bourbaki, Vol. 4, Soc. Math. France, Paris, 1995, pp. Exp. No. 144, 95 – 110 (French).
[7] Lynn H. Loomis, An introduction to abstract harmonic analysis, D. Van Nostrand Company, Inc., Toronto-New York-London, 1953. · Zbl 0052.11701
[8] 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
[9] Hans Reiter, Classical harmonic analysis and locally compact groups, Clarendon Press, Oxford, 1968. · Zbl 0165.15601
[10] Laurent Schwartz, Théorie des distributions, Publications de l’Institut de Mathématique de l’Université de Strasbourg, No. IX-X. Nouvelle édition, entiérement corrigée, refondue et augmentée, Hermann, Paris, 1966 (French). · Zbl 0962.46025
[11] François Bruhat, Distributions sur un groupe localement compact et applications à l’étude des représentations des groupes ℘-adiques, Bull. Soc. Math. France 89 (1961), 43 – 75 (French). · Zbl 0128.35701
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