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Tight Frames of Polynomials and the Truncated Trigonometric Moment Problem (1994)

Gabardo, Jean-Pierre

Springer

The journal of Fourier analysis and applications 1 (1994), S. 249-279

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ISSN: 1531-5851

Source: Springer Online Journal Archives 1860-2000

Topics: Mathematics

Notes: Abstract A simple parametrization is given for the set of positive measures with finite support on the circle group T that are solutions of the truncated trigonometric moment problem: $\hat{\mu}(k)=s_k, |k|\le N,$ where the parameters are, up to nonzero multiplicative constants, the polynomials whose roots all have a modulus less than one. This result is then used to characterize, on a certain natural Hilbert space of polynomials associated with the problem, all finite "weighted" tight frames of evaluation polynomials. Finally, a new and simple way of parametrizing the whole set of positive Borel measures on T, solutions of the given moment problem is deduced, via a limiting argument.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/s00041-001-4012-9

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