Constructing pairs of dual bandlimited framelets with desired time localization

Constructing pairs of dual bandlimited framelets with desired time localization

Constructing Pairs of Dual Bandlimited Frame Wavelets in L(r)

Given a real, expansive dilation matrix we prove that any bandlimited function ψ ∈ L(R), for which the dilations of its Fourier transform form a partition of unity, generates a wavelet frame for certain translation lattices. Moreover, there exists a dual wavelet frame generated by a finite linear combination of dilations of ψ with explicitly given coefficients. The result allows a simple constr...

Constructing pairs of dual bandlimited frame wavelets in L^2(R^n)

Given a real, expansive dilation matrix we prove that any bandlimited function ψ ∈ L(R), for which the dilations of its Fourier transform form a partition of unity, generates a wavelet frame for certain translation lattices. Moreover, there exists a dual wavelet frame generated by a finite linear combination of dilations of ψ with explicitly given coefficients. The result allows a simple constr...

Pairs of Dual Gabor Frame Generators with Compact Support and Desired Frequency Localization

Let g ∈ L2(R) be a compactly supported function, whose integertranslates {Tkg}k∈Z form a partition of unity. We prove that for certain translationand modulation parameters, such a function g generates a Gabor frame, with a (non-canonical) dual generated by a finite linear combination h of the functions {Tkg}k∈Z; the coefficients in the linear combination are given explicitly. Thus, h has compac...

Constructing Minimal Pairs of Degrees

We prove that there exist sets of natural numbers A and B such that A and B form a minimal pair with respect to Turing reducibility, enumeration reducibility, hyperarithmetical reducibility and hyperenumer-ation reducibility. Relativized versions of this result are presented as well. 1. Introduction In the present paper we consider four kinds of reducibilities among sets of natural numbers: Tur...