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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Simple example of nonuniqueness for a dual trigonometric series
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by Robert B. Kelman PDF
Proc. Amer. Math. Soc. 78 (1980), 245-246 Request permission

Abstract:

A simple nonzero solution is given for the classic homogeneous dual trigonometric equation having the kernel $\{ \sin (n + 1/2)x\}$. The solution’s rate of growth is minimal.
References
  • Robert B. Kelman, A Dirichlet-Jordan theorem for dual trigonometric series, Pacific J. Math. 59 (1975), no. 1, 113–123. MR 397277
  • T. M. MacRobert, Spherical harmonics. An elementary treatise on harmonic functions with applications, International Series of Monographs in Pure and Applied Mathematics, Vol. 98, Pergamon Press, Oxford-New York-Toronto, Ont., 1967. Third edition revised with the assistance of I. N. Sneddon. MR 0220985
  • R. P. Srivastav, Dual series relations. V. A generalized Schlömilch series and the uniqueness of the solution of dual equations involving trigonometric series, Proc. Roy. Soc. Edinburgh Sect. A 66 (1963/64), 258–268 (1965). MR 173906
  • A. Zygmund, Trigonometric series: Vols. I, II, Cambridge University Press, London-New York, 1968. Second edition, reprinted with corrections and some additions. MR 0236587
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Additional Information
  • © Copyright 1980 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 78 (1980), 245-246
  • MSC: Primary 42A63
  • DOI: https://doi.org/10.1090/S0002-9939-1980-0550505-5
  • MathSciNet review: 550505