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Bulletin of the London Mathematical Society 2001 33(5):599-605; doi:10.1112/S0024609301008268
© 2001 by London Mathematical Society
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© London Mathematical Society

On an Extension Problem for Polynomials

Mihály Bakonyi and Dan Timotin

Department of Mathematics, Georgia State University Atlanta, Georgia 30303, U.S.A. mbakonyi{at}cs.gsu.edu
Institute of Mathematics of the Romanian Academy P.O. Box 1-764, Bucharest 70700, Romania; dtimotin{at}imar.ro

Received 12 October 1999. Revision received 12 August 2000.

Consider the following problem: given complex numbers a1, ..., an, find an L{infty} function f of minimum norm whose Fourier coefficients ck(f) are equal to ak for k between 0 and n. We show the uniqueness of this function, and we estimate its norm. The operator-valued case is also discussed. 2000 Mathematics Subject Classification 30E05, 47A20, 47A56, 47A57.


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