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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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
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?)

  • [1] Robert B. Kelman, A Dirichlet-Jordan theorem for dual trigonometric series, Pacific J. Math. 59 (1975), no. 1, 113–123. MR 0397277 (53 #1136)
  • [2] T. M. MacRobert, Spherical harmonics. An elementary treatise on harmonic functions with applications, Third edition revised with the assistance of I. N. Sneddon. International Series of Monographs in Pure and Applied Mathematics, Vol. 98, Pergamon Press, Oxford-New York-Toronto, Ont., 1967. MR 0220985 (36 #4037)
  • [3] 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 (1963/1964), 258–268 (1965). MR 0173906 (30 #4113)
  • [4] A. Zygmund, Trigonometric series: Vols. I, II, Second edition, reprinted with corrections and some additions, Cambridge University Press, London-New York, 1968. MR 0236587 (38 #4882)

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1980-0550505-5
PII: S 0002-9939(1980)0550505-5
Article copyright: © Copyright 1980 American Mathematical Society