Abstract. A Weyl-Heisenberg frame for L(R) is a frame consisting of translates and modulates of a fixed function in L(R), i.e. (EmbTnag)m,n∈Z , with a, b > 0, and g ∈ L(R). In this paper we will give necessary and sufficient conditions for this family to form a tight WH-frame. This allows us to write down explicitly all functions g so that (EmbTnag) is an orthonormal basis for L (R). These resu...

We discuss the concepts of pseudo-dual frames and approximately dual frames, and illuminate their relationship to classical frames. Approximately dual frames are easier to construct than the classical dual frames, and might be tailored to yield almost perfect reconstruction. For approximately dual frames constructed via perturbation theory, we provide a bound on the deviation from perfect recon...

For Gabor sets, (g; a, b), it is known that (g; a, b) is a frame if and only if (g; 1/b, 1/a) is a Riesz basis for its span. In particular, for every g there is a0 such that for every a < a0, there is a bm = bm(a) > 0 so that for every b < bm, (g; a, b) is a frame, and (g; 1/b, 1/a) is a Riesz basis sequence. In this talk we shall consider a similar problem for wavelet sets (Ψ; a, b). The main ...

We describe a procedure that enables us to construct dual pairs of wavelet frames from certain dual pairs of Gabor frames. Applying the construction to Gabor frames generated by appropriate exponential Bsplines gives wavelet frames generated by functions whose Fourier transforms are compactly supported splines with geometrically distributed knot sequences. There is also a reverse transform, whi...

A new class of alternative dual frames is introduced in the setting of finite frames for Rd. These dual frames, called Sobolev duals, provide a high precision linear reconstruction procedure for Sigma-Delta (Σ∆) quantization of finite frames. The main result is summarized as follows: reconstruction with Sobolev duals enables stable rth order Sigma-Delta schemes to achieve deterministic approxim...

in this paper, we first show that the tensor product of a finite number of standard g-frames (resp. fusion frames, frames) is a standard g-frame (resp. fusion frame, frame) for the tensor product of hilbert $c^ast-$ modules and vice versa, then we consider tensor products of g-bessel multipliers, bessel multipliers and bessel fusion multipliers in hilbert $c^ast-$modules. moreover, we obtain so...

In this paper, we first show that the tensor product of a finite number of standard g-frames (resp. fusion frames, frames) is a standard g-frame (resp. fusion frame, frame) for the tensor product of Hilbert $C^ast-$ modules and vice versa, then we consider tensor products of g-Bessel multipliers, Bessel multipliers and Bessel fusion multipliers in Hilbert $C^ast-$modules. Moreover, we obtain so...