Let ψ : [0, 1] → R be a strictly increasing continuous function. Let Pn be a polynomial of degree n determined by the biorthogonality conditions ∫ 1 0 Pn (x)ψ (x) j dx = 0, j = 0, 1, . . . , n− 1. We study the distribution of zeros of Pn as n → ∞, and related potential theory.

A generalization of Schauder basis associated with the concept of generalized analytic functions is introduced. Corresponding concepts of density, completeness, biorthogonality and basicity are defined. Also, corresponding concept of the space of coefficients is introduced. Under certain conditions for the  corresponding operators, some properties of the space of coefficients and basicity crite...

We construct a family of continuous biorthogonal functions related to an elliptic analogue of the Gauss hypergeometric function. The key tools used for that are the elliptic beta integral and the integral Bailey chain introduced earlier by the author. Relations to the Sklyanin algebra and elliptic analogues of the Faddeev modular double are discussed in detail.

A family of continuous biorthogonal functions related to an elliptic analog of the Gauss hypergeometric function is constructed. The key tools used for that are the elliptic beta integral and the integral Bailey chain introduced earlier by the author. The relationship with the Sklyanin algebra and elliptic analogs of the Faddeev modular double are discussed in detail. §

This paper is devoted to the analysis of the behaviour, in nite precision arithmetic, of the quasi-minimal residual method without look ahead for the solution of linear systems Ax = b where A is a real or complex matrix of order n. In exact arithmetic, the behaviour of the method as applied to symmetric deenite matrices is well understood; but results about convergence usually suppose that the ...

We analyze polarization changes of light diffracted on a planar chiral array from the standpoint of the Lorentz reciprocity lemma and find biorthogonality in the polarization eigenstates for waves diffracting though the grating in the opposite direction. Both reciprocal and nonreciprocal components in the polarization azimuth rotation of the diffracted light are identified. The structural chira...

We define operational logical relations between terms of a polymorphically typed functional language and low-level programs for a variant SECD machine. The relations, defined using biorthogonality and step-indexing, give extensional and compositional specifications expressing when low-level code and machine values realize typed source-level terms. We prove the correctness of a compiler and of s...

In this paper we introduce an algorithm for the construction of compactly supported interpolating scaling vectors on Rd with certain symmetry properties. In addition, we give an explicit construction method for corresponding symmetric dual scaling vectors and multiwavelets. As the main ingredients of our recipe we derive some implementable conditions for accuracy, symmetry, and biorthogonality ...

In 1996, we constructed periodic interpolatory scaling functions φj , wavelet functions Lj and their dual basis φ̃j and L̃j with properties such as symmetry, biorthogonality, any order of smoothness, real-valuedness, explicit expressions and interpolatory. We proved the localization of φj in 1997, and in 1998 with Li proved the localization of Lj . In this paper we shall give a detailed proof of ...

We introduce families of rational functions that are biorthogonal with respect to the $q$-hypergeometric distribution. A triplet $q$-difference operators $X$, $Y$, $Z$ is shown play a role analogous pair bispectral orthogonal polynomials. The recurrence relation and difference equation take form generalized eigenvalue problems involving three operators. algebra generated by akin algebras Askey-...