Weighted quadratic norms and ultraspherical polynomials. I
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- by Richard Askey and Isidore Hirschman
- Trans. Amer. Math. Soc. 91 (1959), 294-313
- DOI: https://doi.org/10.1090/S0002-9947-1959-0107772-5
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References
- S. Bochner, Positive zonal functions on spheres, Proc. Nat. Acad. Sci. U.S.A. 40 (1954), 1141–1147. MR 68127, DOI 10.1073/pnas.40.12.1141 A. Erdelyi et al., Higher transcendental functions, New York, 1953.
- I. I. Hirschman, The decomposition of Walsh and Fourier series, Mem. Amer. Math. Soc. 15 (1955), 65. MR 72269
- I. I. Hirschman Jr., Weighted quadratic norms and Legendre polynomials, Canadian J. Math. 7 (1955), 462–482. MR 73731, DOI 10.4153/CJM-1955-050-x
- I. I. Hirschman Jr., A note on orthogonal systems, Pacific J. Math. 6 (1956), 47–56. MR 79129, DOI 10.2140/pjm.1956.6.47 —, Harmonic analysis and ultraspherical polynomials, Proceedings of the Conference on Harmonic Analysis, Cornell, 1956.
- B. M. Lewitan, A generalization of the operation of translation and infinite hypercomplex systems. II, Rec. Math. [Mat. Sbornik] N.S. 17 (59) (1945), 9–44 (English, with Russian summary). MR 0014214
- Hsien-yü Hsü, Certain integrals and infinite series involving ultra-spherical polynomials and Bessel functions, Duke Math. J. 4 (1938), no. 2, 374–383. MR 1546058, DOI 10.1215/S0012-7094-38-00429-6
- Jerome Newman and Walter Rudin, Mean convergence of orthogonal series, Proc. Amer. Math. Soc. 3 (1952), 219–222. MR 47811, DOI 10.1090/S0002-9939-1952-0047811-2
- Harry Pollard, The mean convergence of orthogonal series. II, Trans. Amer. Math. Soc. 63 (1948), 355–367. MR 23941, DOI 10.1090/S0002-9947-1948-0023941-X A. Zygmund, Trigonometrical series, Warsaw-Lwow, 1935. G. Szegö, Orthogonal polynomials, New York, 1939.
Bibliographic Information
- © Copyright 1959 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 91 (1959), 294-313
- MSC: Primary 41.00; Secondary 44.00
- DOI: https://doi.org/10.1090/S0002-9947-1959-0107772-5
- MathSciNet review: 0107772