Tight Frames of Polynomials and the Truncated Trigonometric Moment Problem |
| |
Authors: | Jean-Pierre Gabardo |
| |
Institution: | (1) Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario, L8S 4K1, Canada |
| |
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:
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. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|