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\(\ell^1\)-convolution algebras: Representation and factorization. (English) Zbl 0357.43004


MSC:

43A20 \(L^1\)-algebras on groups, semigroups, etc.
46J99 Commutative Banach algebras and commutative topological algebras
46A45 Sequence spaces (including Köthe sequence spaces)
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[1] Askey, R., Gasper, G.: Linearization of the product of Jacobi Polynomials. III. Canadian J. Math. 23, 332-338 (1971) · Zbl 0212.40904 · doi:10.4153/CJM-1971-033-6
[2] Bingham, N.H.: Positive definite functions on spheres. Proc. Cambridge Philos. Soc. 73, 145-156 (1973) · Zbl 0244.43002 · doi:10.1017/S0305004100047551
[3] Favard, J.: Sur les polynomes de Tchebicheff. C.R. Acad. des Sci. Paris, Sér. A-B 200, 2052-2053 (1935) · JFM 61.0288.01
[4] Gasper, G.: Positivity and special functions. Theory and Applications of Special Functions, R. Askey ed., pp. 375-433. New York: Academic Press 1975 · Zbl 0326.33009
[5] Gilewski, J.: Generalized convolutions and delphic semigroups. Colloq. Math. 25, 281-289 (1972) · Zbl 0252.22006
[6] Gilewski, J., Urbanik, K.: Generalized convolutions and generating functions. Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 16, 481-487 (1963) · Zbl 0192.53601
[7] Hirschman, I.I., Jr.: Harmonic analysis and ultraspherical polynomials. Symposium on Harmonic Analysis and Related Integral Transform. Cornell University 1956
[8] Hirschman, I.I., Jr.: Sur les polynomes ultrasphériques. C.R. Acad. Sci. Paris Sér. A-B 242, 2212-2214 (1956) · Zbl 0071.06102
[9] Kendall, D.G.: Delphic semi-groups, infinitely divisible regenerative phenomena, and the arithmetic of p-functions. Z. Wahrscheinlichkeitstheorie verw. Gebiete 9, 163-195 (1968) · Zbl 0159.46902 · doi:10.1007/BF00535637
[10] Lamperti, J.: The arithmetic of certain semi-groups of positive operators. Proc. Cambridge Philos. Soc. 64, 161-166 (1968) · Zbl 0159.47001 · doi:10.1017/S0305004100042675
[11] Linnik, Yu.V.: Decomposition of probability distributions. Edinburgh: Oliver and Boyd 1964 · Zbl 0121.35502
[12] Lukacs, E.: Characteristic Functions. New York: Hafner 1970 · Zbl 0201.20404
[13] Rudin, W.: Real and Complex Analysis. New York: McGraw Hill 1974 · Zbl 0278.26001
[14] Schwartz, A.L.: Generalized convolutions and positive definite functions associated with general orthogonal series. Pacific J. Math. 55, 565-582 (1974) · Zbl 0314.33006
[15] Shohat, J.: The relation of the classical orthogonal polynomials to the polynomials of Appell. Amer. J. Math. 58, 453-464 (1936) · Zbl 0014.30802 · doi:10.2307/2370962
[16] Szego, G.: Orthogonal Polynomials. Amer. Math. Soc. Colloq. Pub., 23. Providence: American Mathematical Society 1967
[17] Urbanik, K.: Generalized convolutions. Studia Math. 23, 217-245 (1964) · Zbl 0171.39504
[18] Urbanik, K.: Generalized convolutions II. Studia Math. 45, 57-70 (1973) · Zbl 0283.60017
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