On continuous weaving frames

摘要

Two discrete frames {ф_i}_(i?I) and {ψ_i}_(i?I) for a separable Hilbert space H are said to be woven if there are universal positive constants A and B such that for every subset σ? I, the family {ф_i}_(i?σ) ∈{ψ_i}_(i?σ~c)is a frame forHwith lower and upper frame bounds A and B, respectively.Weaving frames are powerful tools in pre-processing signals and distributed data processing. Motivated by the recent work of Bemrose–Casazza– Gr?chenig–Lammers–Lynch and Casazza–Lynch on weaving frames for separable Hilbert spaces, we study continuous weaving frames for Hilbert spaces with respect to a measure space. In this paper, first we present two necessary conditions in terms of frame bounds for continuous weaving frames. A sufficient condition for continuous weaving frames is given. We provide an estimate of a series associated with the metric operators of continuous weaving frames. Finally, two Paley–Wiener-type perturbation results for continuous weaving frames are given.