we define a new function-valued inner product on l2(g), called ?-bracket product, where g is a locally compact abelian group and ? is a topological isomorphism on g. we investigate the notion of ?-orthogonality, bessel's inequality and ?-orthonormal bases with respect to this inner product on l2(g).

Abstract We present a dimension-incremental algorithm for the nonlinear approximation of high-dimensional functions in an arbitrary bounded orthonormal product basis. Our goal is to detect suitable truncation basis expansion function, where corresponding support assumed be unknown. method based on point evaluations considered function and adaptively builds index set such that approximately larg...

| This paper develops a general and very simple construction for complete orthonormal bases for system identiica-tion. This construction provides a unifying formulation of many previously studied orthonormal bases since the common FIR and recently popular Laguerre and two-parameter Kautz model structures are restrictive special cases of the construction presented here. However, in contrast to t...

We consider the modeling of non-stationary discrete signals whose amplitude and frequency are assumed to be nonlinearly modulated over very short-time duration. We investigate the case where both instantaneous amplitude and frequency can be approximated by orthonormal polynomials. Previous works dealing with polynomial approximations refer to orthonormal bases built from a discretization of con...

A number of constructions in function field arithmetic involve extensions from linear objects using digit expansions. This technique is described here as a method of constructing orthonormal bases in spaces of continuous functions. We illustrate several examples of orthonormal bases from this viewpoint, and we also obtain a concrete model for the continuous functions on the integers of a local ...

in this paper, the numerical technique based on hybrid bernoulli and block-pulse functions has been developed to approximate the solution of system of linear volterra integral equations. system of volterra integral equations arose in many physical problems such as elastodynamic, quasi-static visco-elasticity and magneto-electro-elastic dynamic problems. these functions are formed by the hybridi...

Existing work on the representation of operators in one-dimensional, compactly-supported, orthonormal wavelet bases is extended to two dimensions. The non-standard form of the representation of operators is given in separable two-dimensional, periodic, orthonormal wavelet bases. The matrix representation of the partial differential operators ∂x and ∂y are constructed and a closed form formula f...

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...