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...

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...

A compact domain in R n is a spectral set if there is some subset of R n such that fexp(2ih; xi) : 2 g when restricted to gives an orthogonal basis of L 2 ((). The set is called a spectrum for. We give a criterion for being a spectrum of a given set in terms of tiling Fourier space by translates of a suitable auxiliary set D. We apply this criterion to classify all spectra for the n-cube by sho...

In this paper we develop a general and very simple construction for complete orthonormal bases for system identiication. This construction provides a unifying formulation of all known orthonormal bases since the common FIR and recently popular Laguerre and Kautz model structures are restrictive special cases of our construction as is another construction method based on balanced realisations of...

In this paper, model sets for continuous{time linear time invariant systems that are spanned by xed pole orthonormal bases are investigated. These bases gen-eralise the well known Laguerre and Kautz bases. It is shown that the obtained model sets are complete in all of the Hardy spaces H p ((); 1 p < 1 and the right half plane algebra A(() provided that a mild condition on the choice of basis p...