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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2024 MCQ for Transactions of the American Mathematical Society is 1.48 .

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The mean convergence of orthogonal series. I
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by Harry Pollard
Trans. Amer. Math. Soc. 62 (1947), 387-403
DOI: https://doi.org/10.1090/S0002-9947-1947-0022932-1
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References
  • Marcel Riesz, Sur les fonctions conjuguées, Math. Z. 27 (1928), no. 1, 218–244 (French). MR 1544909, DOI 10.1007/BF01171098
  • Juljusz Schauder, Eine Eigenschaft des Haarschen Orthogonalsystems, Math. Z. 28 (1928), no. 1, 317–320 (German). MR 1544958, DOI 10.1007/BF01181164
  • H. Kober, A note on approximation by rational functions, Proc. Edinburgh Math. Soc. (2) 7 (1946), 123–133. MR 15556, DOI 10.1017/S001309150002441X
  • W. B. Caton and E. Hille, Laguerre polynomials and Laplace integrals, Duke Math. J. 12 (1945), 217–242. MR 12166
  • Harry Pollard, The mean convergence of orthogonal series of polynomials, Proc. Nat. Acad. Sci. U.S.A. 32 (1946), 8–10. MR 14499, DOI 10.1073/pnas.32.1.8
    • G. H. Hardy, J. E. Littlewood, and G. Pólya, Inequalities, Cambridge, 1933. E. Hille, Some problems concerning spherical harmonics, Arkiv for Matematik, Astronomi och Fysik vol. 13 (1918) pp. 1-76. S. Banach, Théorie des opérations linéaires, Warsaw, 1932.
  • Norman Levinson, Gap and Density Theorems, American Mathematical Society Colloquium Publications, Vol. 26, American Mathematical Society, New York, 1940. MR 0003208
    • A. Zygmund, Trigonometrical series, Warsaw, 1935. G. Szegö, Orthogonal polynomials, Amer. Math. Soc. Colloquium Publications, vol. 23, New York, 1939. E. W. Watson, The theory of spherical and ellipsoidal harmonics, Cambridge, 1931.
  • R. P. Boas Jr. and Harry Pollard, Complete sets of Bessel and Legendre functions, Ann. of Math. (2) 48 (1947), 366–384. MR 20660, DOI 10.2307/1969177
    • R. E. A. C. Paley, A remarkable system of orthogonal functions, Proc. London Math. Soc. vol. 34 (1932) pp. 241-279.
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Bibliographic Information
  • © Copyright 1947 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 62 (1947), 387-403
  • MSC: Primary 42.4X
  • DOI: https://doi.org/10.1090/S0002-9947-1947-0022932-1
  • MathSciNet review: 0022932