Shannon wavelets are used to define a method for the solution of integrodifferential equations. This method is based on 1 the Galerking method, 2 the Shannon wavelet representation, 3 the decorrelation of the generalized Shannon sampling theorem, and 4 the definition of connection coefficients. The Shannon sampling theorem is considered in a more general approach suitable for analysing function...

This paper is concerned with obtaining the approximate solution of Fredholm-Volterra integro-differential equations. Properties of the Shannon wavelets and connection coefficients are first presented. We design a numerical scheme for these equations using the Galerkin method incorporated with the Shannon wavelets approximation and the connection coefficients. We will show that using this techni...

This paper details the development of the weak form formulations of finite element type methods using wavelets as basis functions. Such approaches are different from most wavelets based ones that are derived from the strong form. The advantages of the proposed formulation are that there is no need to enforce natural boundary conditions and that the lower order derivatives of the wavelet bases a...

A 'differential measure' is used to cast our calculus for the group SU (3) into a form similar to Schwinger's boson operator calculus for the group SU (2). It is then applied to compute (i) the inner product between the basis states and (ii) an algebraic formula for the Clebsch-Gordan coefficients. These were obtained earlier by us using Gaussian integration techniques.

The zero distribution of orthogonal polynomials pn,N , n = 0, 1, . . . generated by recurrence coefficients an,N and bn,N depending on a parameter N has been recently considered by Kuijlaars and Van Assche under the assumption that an,N and bn,N behave like a(n/N) and b(n/N), respectively, where a(·) and b(·) are continuous functions. Here, we extend this result by allowing a(·) and b(·) to be ...

The purpose of this paper is to find out a set of general recurrence formulas for the calculus of the SU(3) Clebsch-Gordan coefficients. The first six sections are introductory, presenting the notations and general group theoretical methods applied to SU(3). The following eight sections are devoted to a detailed treatment of the carrier spaces of the irreducible representations and their direct...