Orthogonal polynomials for two different ranges
On Koornwinder classical orthogonal polynomials in two variables
... of two-variables analogues of the Jacobi polynomials, and he introduced seven classes of orthogonal polynomials in two variables obtained from Jacobi ...as two-variable analogues ...
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Two variable orthogonal polynomials and structured matrices
... between orthogonal polynomials and the Hankel or Toeplitz matrices associated with them plays an important role in the ...the orthogonal polynomials give a param- eterization of positive ...
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TURÁN INEQUALITIES AND ZEROS OF ORTHOGONAL POLYNOMIALS. be a family of orthogonal polynomials
... establish two new sets of T I and give second order bounds for a vast class of orthogonal polynomials satisfying (5) with a nondecreasing sequence c k ...
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Mixed type multiple orthogonal polynomials for two Nikishin systems
... NIKISHIN SYSTEMS U. FIDALGO PRIETO, A. L ´ OPEZ GARC´IA, G. L ´ OPEZ LAGOMASINO, AND V. N. SOROKIN Abstract. We study the logarithmic and ratio asymptotics of linear forms constructed from a Nikishin system which satisfy ...
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Two-variable orthogonal polynomials of big q-Jacobi type
... of orthogonal polynomials in two discrete variables is defined for a weight function of basic hypergeometric ...The polynomials, which are expressed in terms of univariate big q-Jacobi ...
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Orthogonal polynomials, paraorthogonal polynomials and point perturbation
... ; τ 1 = (1 − |L| 2 ) 1/2 λ 1 . (7.4.62) Since the matrix on the left hand side of (7.4.62) has a non-zero vector in its kernel, it must have rank 1, so the two rows are equivalent. For that reason we only have to ...
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When do linear combinations of orthogonal polynomials yield new sequences of orthogonal polynomials?
... h k (x) , where h k is a polynomial of degree k positive on (−1, 1) and µ j is the Chebyshev weight of j–th kind, (j = 1, 2, 3, 4). The aim of this work is to analyze linear combinations with constant coef- ficients Q n = ...
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On zeros of discrete orthogonal polynomials
... symmetric orthogonal polynomials sharp second order asymptotics and inequalities are known in terms of the three term recurrence relation ...Krawtchouk polynomials they yield bounds very similar, in ...
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Poisson brackets of orthogonal polynomials
... d y 1 ∧ . . . ∧ dy k . (7.3) Our goal here is to compute the two Jacobians | ∂(a,b) ∂(x,ρ) | for OPRL and | ∂(Re α,Im α) ∂(θ,µ) | for OPUC. It appears that these were first found for OPRL by Dumitriu–Edelman [12], ...
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Generalized hypergroups and orthogonal polynomials
... Later on results of harmonic analysis on hypergroups were transferred to different applica- tions. For example a Bochner theorem is used essentially in the context of weakly stationary processes indexed by ...
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A conjecture on exceptional orthogonal polynomials
... m orthogonal polynomial system for m ≤ 2 can be obtained by applying a sequence of at most m Darboux transformations to a classical orthogonal polynomial ...codimension two flags contain free ...
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Classes of Bivariate Orthogonal Polynomials
... gave two q-analogues of the 2D-Hermite polynomials and studied the polynomials in great ...a different q-analogue of the disc ...of two variable polynomials whose measure is the ...
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Matrix orthogonal polynomials whose derivatives are also orthogonal
... The proofs of the above equivalences are given for any sequence of MOP, not necessarily related to a hermitian weight matrix. The Pearson-type equation involves a distributional derivative. The distributional definition ...
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Asymptotics of multiple orthogonal polynomials for a system of two measures supported on a starlike set
... of two measures supported on a starlike set in the complex plane, we study the asymptotic properties of the associated multiple orthogonal polynomials Q n and their recurrence ...the ...
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A finite family of q-orthogonal polynomials and resultants of Chebyshev polynomials
... to orthogonal polynomials and special functions are con- ...q-Jacobi polynomials are orthogonal on the imaginary ...of polynomials that are orthogonal on ...q-Jacobi ...
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Asymptotic Properties of Orthogonal and Extremal Polynomials
... The physical intuition behind the equilibrium distribution is quite simple. In two dimensions, the electrostatic interaction is given by a logarithmic repulsion. Therefore, if a large collection of charged ...
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Darboux Transforms and 2-Orthogonal Polynomials
... The main purpose of this paper is to present a new interpretation of Darboux transforms in the context of 2− orthogonal polynomials. The paper essentially consists of two sections. Following the ...
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On conjectures of Stenger in the theory of orthogonal polynomials
... For illustration, we show in Fig. 18 the eigenvalues in the cases (N, n) = (2, 30), (6, 28), (10, 25), the last two containing a pair of eigenvalues with negative real part. The presence of delinquent eigenvalues ...
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A class of orthogonal polynomials of a new type
... ential equations, two Rodrigues’ formulas and two recurrence relations for even and odd values of the variable parameter and associated in the same function space, was.. obtained, and st[r] ...
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On Certain Wronskians of Multiple Orthogonal Polynomials
... give two applications of our main ...characteristic polynomials for multiple orthogonal polynomial ensembles can be expressed as a Wronskian of the type II multiple orthogonal ...multiple ...
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