finite normalized tight frames are interesting because they provide decompositionsin applications and some physical interpretations. in this article,we give a recursive method for constructing them.

In this paper, we establish several new inequalities for g-frames in Hilbert C∗ -modules which are different in structure from those previously obtained by Balan et al. for Hilbert space frames. We also present some equalities and inequalities for g-frames in Hilbert C∗ -modules with Moore–Penrose inverses and show that they are more general and cover some results in [Xiao, XC, Zeng, XM: Some p...

We investigate the relevance of admissibility criteria based on Plancherel measure for the characterization of tight Weyl-Heisenberg frames with integer oversampling. For this purpose we observe that functions giving rise to such Weyl-Heisenberg frames are admissible with regard to the action of a suitably defined type-I discrete group G. This allows to relate the construction of Weyl-Heisenber...

Up to unitary equivalence, there are a finite number of tight frames of n vectors for C which can be obtained as the orbit of a single vector under the unitary action of an abelian group G (for nonabelian groups there may be uncountably many). These so called harmonic frames (or geometrically uniform tight frames) have recently been used in applications including signal processing (where G is t...

Frames for Hilbert spaces were first introduced by Duffin and Schaeffer [10] in 1952 to study some problems in nonharmonic Fourier series, reintroduced in 1986 by Daubechies, Grossmann and Meyer [8]. Frames are very useful in characterization of function spaces and other fields of applications such as filter bank theory, sigmadelta quantization, signal and image processing and wireless communic...

This work presents a quantitative framework for describing the overcompleteness of a large class of frames. It introduces notions of localization and approximation between two frames F = {fi}i∈I and E = {ej}j∈G (G a discrete abelian group), relating the decay of the expansion of the elements of F in terms of the elements of E via a map a : I → G. A fundamental set of equalities are shown betwee...