Frames by Multiplication

P. BALAZS, C. CABRELLI, S. HEINEKEN AND U. MOLTER

Current Developments in Theory and Applications of Wavelets

Pushpa Publishing House

Año: 2011 vol. 5 p. 165 - 186

0973-5607

In this note we study frame-related properties of a sequence of functions multiplied by another function. In particular we study frame and Riesz basis properties. We apply these results to sets of irregular translates of a bandlimited function h in L2(Rd). This is achieved by lookingat a set of exponentials restricted to a set E ⊂Rd with frequencies ina countable set Λ and multiplying it by the Fourier transform of a fixed function h ∈ L2(E). Using density results due to Beurling, we prove the existence and give ways to construct frames by irregular translates.