Representation of the inverse of a multiplier as a multiplier

Details Representation of the inverse of a multiplier as a multiplier Representation of the inverse of a multiplier as a multiplier

2011-08-31

arxiv.org/abs/1108.6286v1

Mathematics

Functional Analysis

Scientific paper

Frame multipliers are interesting mathematical objects consisting of analysis, multiplication by a fixed sequence (called the symbol), and synthesis. Since they are important for applications, for example for the realization of time-varying filters, their inversion is of interest. For Riesz bases and semi-normalized symbols, it is known that the inverse of the multiplier can be found by using the biorthogonal sequences and the reciprocal symbol. In this paper we extend the class of multipliers where the inverse is represented by a multiplier. In particular, we show that for semi-normalized symbols any invertible frame multiplier can be represented as a frame multiplier with dual sequences. Furthermore, we give sufficient conditions, so that the inverse involves the reciprocal symbol and the canonical duals.

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