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Simple example of nonuniqueness for a dual trigonometric series


Author: Robert B. Kelman
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
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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 [Enhancements On Off] (What's this?)

  • 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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Article copyright: © Copyright 1980 American Mathematical Society