On the trigonometric conjugate to the general Franklin system
We investigate when the trigonometric conjugate to the periodic general Franklin system is a basis in C(𝕋). For this, we find some necessary and some sufficient conditions.
On three problems from the Scottish Book connected with orthogonal systems
On zeros of reciprocal polynomials of odd degree.
On zeros of regular orthogonal polynomials on the unit circle
A new approach to the study of zeros of orthogonal polynomials with respect to an Hermitian and regular linear functional is presented. Some results concerning zeros of kernels are given.
Ondelettes, analyses multirésolutions et filtres miroirs en quadrature
Operators preserving orthogonality of polynomials
Let S be a degree preserving linear operator of ℝ[X] into itself. The question is if, preserving orthogonality of some orthogonal polynomial sequences, S must necessarily be an operator of composition with some affine function of ℝ. In [2] this problem was considered for S mapping sequences of Laguerre polynomials onto sequences of orthogonal polynomials. Here we improve substantially the theorems of [2] as well as disprove the conjecture proposed there. We also consider the same questions for polynomials...
Optimal discrete signal representation by the system of discrete orthonormal exponentials in conjugate pairs of exponents
Orthogonal Algebraic Polynomial Schauder Bases of Optimal Degree.
Orthogonal Laurent polynomials and quadratures on the unit circle and the real half-line.
Orthogonal polynomials.
Orthogonal polynomials and quadratic transformations.
Orthogonal Polynomials and Regularly Varying Sequences
Orthogonal polynomials and the Lanczos method
Lanczos method for solving a system of linear equations is well known. It is derived from a generalization of the method of moments and one of its main interests is that it provides the exact answer in at most n steps where n is the dimension of the system. Lanczos method can be implemented via several recursive algorithms known as Orthodir, Orthomin, Orthores, Biconjugate gradient,... In this paper, we show that all these procedures can be explained within the framework of formal orthogonal polynomials....
Orthogonal Polynomials, L2-Spaces and Entire Functions.
Orthogonal -polynomials related to perturbed linear form.
Orthonormal polynomial vectors and least squares approximation for a discrete inner product.