By the use of locally supported basis functions for spherical spline interpolation the applicability of this approximation method is spread out since the resulting interpolation matrix is sparse and thus eecient solvers can be used. In this paper we study locally supported kernels in detail. Investigations on the Legendre coeecients allow a characterization of the underlying Hilbert space struc...

Orthogonal moments are recognized as useful tools for object representation and image analysis. It has been shown that the recently developed discrete orthogonal moments have better performance than the conventional continuous orthogonal moments. In this paper, a new set of discrete orthogonal polynomials, namely Hahn polynomials, are introduced. The related Hahn moment functions defined on thi...

This paper deals with Szegö type limits for multiplication operators on L(R) with respect to Haar orthonormal basis. Similar studies have been carried out by Morrison for multiplication operators Tf using Walsh System and Legendre polynomials [14]. Unlike the Walsh and Fourier basis functions, the Haar basis functions are local in nature. It is observed that Szegö type limit exist for a class o...

The classical orthogonal functions of mathematical physics are closely related to Lie groups. Specifically, they are matrix elements of, or basis vectors for, unitary irreducible representations of lowdimensional Lie groups. We illustrate this connection for: The Wigner functions, spherical harmonics, and Legendre polynomials; the Bessel functions; and the Hermite polynomials. These functions a...

We analyze transient heat conduction in a thick functionally graded plate by using a higher-order plate theory and a meshless local Petrov-Galerkin (MLPG) method. The temperature field is expanded in the thickness direction by using Legendre polynomials as basis functions. For temperature prescribed on one or both major surfaces of the plate, modified Lagrange polynomials are used as basis and ...

Klein/Sine-Gordon equations are very important in that they can accurately model many essential physical phenomena. In this paper, we propose a new spectral method using Legendre wavelets as basis for numerical solution of Klein\Sine-Gordon Equations. Due to the good properties of wavelets basis, the proposed method can obtain good spatial and spectral resolution. Moreover, the presented method...

The aim of this paper is to apply Galerkin weighted residual method for solving eleventh-order BVPs. In this method, we exploit Bernstein and Legendre polynomials as basis functions which are modified into to a new set of basis functions to satisfy the corresponding homogeneous form of boundary conditions where the essential types of boundary conditions are mentioned. The method is formulated a...

The most common approach for approximating non-periodic function defined on a finite interval is based on considering polynomials as basis functions. In this paper we will address the non-optimallity of polynomial approximation and suggest to switch from powers of x to powers of sin(px) where p is a parameter which depends on the dimension of the approximating subspace. The new set does not suf...

To identify the content of motion sequences such as gestures and video sequences, we propose a compact representation of flow fields using a basis of complex Zernike polynomials. Moments derived from projection of these polynomials have been used in recognition. Previously, local descriptions learned from examples, or specified a priori, have been used to identify local flow events. Affine expa...

The usual method of separation of variables to find a basis of solutions of Laplace’s equation in toroidal coordinates is particularly appropriate for axially symmetric applications; for example, to find the potential outside a charged conducting torus. An alternative procedure is presented here that is more appropriate where the boundary conditions are independent of the spherical coordinate y...