In this paper we investigate a new notion of bases in Hilbert spaces and similar to fusion frame theory we introduce fusion bases theory in Hilbert spaces. We also introduce a new denition of fusion dual sequence associated with a fusion basis and show that the operators of a fusion dual sequence are continuous projections. Next we dene the fusion biorthogonal sequence, Bessel fusion basis, Hil...

We give a general approach to in nite dimensional non-Gaussian analysis which generalizes the work [KSWY95]. For given measure we construct a family of biorthogonal systems. We study their properties and their Gel'fand triples that they generate. As an example we consider the measures of Poisson type.

Let φ be an orthonormal scaling function with approximation degree p−1, and let Bn be the B-spline of order n. Then, spline type scaling functions defined by f̄n = f ∗Bn (n = 1, 2, . . . ) possess higher approximation order, p+n−1, and compact support. The corresponding biorthogonal wavelet functions are also constructed. This technique is extended to the case of biorthogonal scaling function sy...

in this paper we develop a natural generalization of schauder basis theory, we term operator-valued basis or simply ov-basis theory, using operator-algebraic methods. we prove several results for ov-basis concerning duality, orthogonality, biorthogonality and minimality. we prove that the operators of a dual ov-basis are continuous. we also de ne the concepts of bessel, hilbert ov-basis and obt...

Computation of pairs of analysis and synthesis (dual) windows is very important in using discrete-time Gabor transform. Biorthogonal-like sequence theory ooers some simple solutions for computing dual windows for signal representation. Solutions to the biorthogonal-like condition are obtained by dividing the problem into various cases. As an example, dual windows for the truncated Gaussian wind...

The problem of solving a system of linear equations is equivalent to the computation of biorthogonal polynomials and to the bordering method which is a procedure for solving recursively a sequence of linear systems with increasing dimensions. In some cases, the biorthogonal polynomials can be computed recursively thus leading to procedures for solving linear systems. The particular cases of Han...

Smooth orthogonal and biorthogonal multiwavelets on the real line with their scaling function vectors being supported on [−1, 1] are of interest in constructing wavelet bases on the interval [0, 1] due to their simple structure. In this paper, we shall present a symmetric C orthogonal multiwavelet with multiplicity 4 such that its orthogonal scaling function vector is supported on [−1, 1], has ...

The paper is devoted to two particular cases of the following general problem. Let α and β be two types of bases in Banach spaces. Let a Banach space X has bases of both types and a subspace M ⊂ X∗ contains the sequence of biorthogonal functionals of some α-basis in X. Does M contain a sequence of biorthogonal functionals of some β-basis in X? The following particular cases are considered: (α, ...

We improve Wang's characterization for a pair of biorthogonal wavelets to be associated with biorthogonal multiresolution analyses (MRA's). We show that one of the two conditions in his characterization is redundant, and, along the way, show that for a pair of biorthogonal wavelets to be associated with biorthogonal MRA's it is necessary and suÆcient that one of the wavelets is associated with ...