The Newton-Lagrange interpolation is a well-known problem in elementary calculus. Recall basic facts concerning this problem [6], [2]. Let Ak, k = 0, 1, 2, . . . and ak, k = 0, 1, 2, . . . be two arbitrary sequences of complex numbers (we assume that all ak are distinct ak 6= aj if k 6= j. By interpolation polynomial we mean a n-degree polynomial Pn(z) whose values at points a0, a1, . . . , an ...

The rise of frame theory in appled mathematics is due to the flexibility and redundancy of frames. Structured frames are much easier to construct than Structured orthonormal bases. In this work, the notion of the ternary generalized multiresolution structure (TGMS) of subspace 2 3 ( ) L R is proposed, which is the generalization of the ternary frame multiresolution analysis. The biorthogonality...

Let α > 0 and ψ (x) = x. Let Sn,α be a polynomial of degree n determined by the biorthogonality conditions Z 1 0 Sn,αψ j = 0, j = 0, 1, . . . , n− 1. We explicitly determine Sn,α and discuss some other properties, including their zero distribution. We also discuss their relation to the Sidi polynomials. §

A new multivariate Toda hierarchy of nonlinear partial differential equations adapted to biorthogonal polynomials is discussed. This integrable associated with non-standard biorthogonality. Wave and Baker functions, linear equations, Lax Zakharov–Shabat KP type appropriate reductions, Darboux or spectral transformations, bilinear involving transformations are presented.

We present a construction of a gradient recovery operator based on an oblique projection, where the basis functions of two involved spaces satisfy a condition of biorthogonality. The biorthogonality condition guarantees that the recovery operator is local. 1. Introduction. One reason for the success of the finite element method for solving partial differential equations is that a reliable a pos...

In this paper we construct a flatlet biorthogonal multiwavelets System. Then, we use this system for numerical solution of Integro-differential equations. The good properties of this system, i.e., biorthogonality and more vanishing moments lead to efficient and accurate solutions. Some test problems with known solutions are presented and the numerical results are given to show the efficiency of...

In this paper, the existence, regularity and biorthogonality of the solution of the nonhomogeneous reenement equation (x) = X k2Z Z d 0 c k (2x ? k) + G(x); x 2 IR d are considered. Also new class of biorthogonal wavelet basis on a non-uniform grid is constructed.

Let G be a countable group of unitary operators on a complex separable Hilbert space H. We give a characterization of biorthogonality among Riesz multiwavelets in terms of certain invariant properties of their associated core spaces. A large family of non-biorthogonal Riesz multiwavelets is exhibited. We also discuss some results on linear perturbation of orthonormal multiwavelets.