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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
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] R. B. Kelman, A Dirichlet-Jordan theorem for dual trigonometric series, Pacific J. Math. 59 (1975), 113-123. MR 0397277 (53:1136)
  • [2] T. M. MacRobert, Spherical harmonics, 3rd ed., Pergamon Press, Oxford, New York, 1967. MR 0220985 (36:4037)
  • [3] R. P. Srivastav, Dual series relations. V. A generalized Schlömlich series and the uniqueness of the solution of dual equations involving trigonometric series, Proc. Roy. Soc. Edinburgh Sect. A 66 (1963-1964), 258-268. MR 0173906 (30:4113)
  • [4] A. Zygmund, Trigonometric series, Vol. 1, 2nd ed., Cambridge University Press, London-New York, 1968. MR 0236587 (38:4882)

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