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Convolutions and zeros of orthogonal polynomials
(Elsevier B.V., 2011-07-01)
In an attempt to answer a long standing open question of Al-Salam we generate various beautiful formulae for convolutions of orthogonal polynomials similar toU(n)(x) = Sigma(n)(k=0) P(k)(x)P(n-k)(x).where U(n)(x) are the ...
Orthogonally additive holomorphic functions of bounded type over C(K)
(Cambridge University Press, 2010-10)
It is known that all k-homogeneous orthogonally additive polynomials P over C(K) are of the form P(x)= ∫Kxkdμ. Thus, x → xk factors all orthogonally additive polynomials through some linear form μ. We show that no such ...
A Characterization of L-orthogonal Polynomials from Three Term Recurrence Relations
(Springer, 2011-01-01)
We consider the sequence of polynomials {Q (n) } satisfying the L-orthogonality a"(3)[z (-n+m) Q (n) (z)]=0, 0a parts per thousand currency signma parts per thousand currency signn-1, with respect to a linear functional ...
Polinômios Multiortogonais
(Universidade Estadual Paulista (Unesp), 2021-07-06)
O objetivo principal desta dissertação é estudar a existência dos Polinômios Multiortogonais do Tipo II e também a equivalência das relações de ortogonalidade dos Polinômios Multiortogonais do Tipo II com as Aproximações ...
Orthogonality of quasi-orthogonal polynomials
(2018-01-01)
A result of Pólya states that every sequence of quadrature formulas Q n (f) with n nodes and positive Cotes numbers converges to the integral I(f) of a continuous function f provided Q n (f) = I(f) for a space of algebraic ...
Finite-dimensional orthogonality structures for hall-littlewood polynomials
(Springer Netherlands, 2008)
Spherical Functions: The Spheres Vs. The Projective Spaces
(Heldermann Verlag, 2014-01)
In this paper we establish a close relationship between the spherical functions of the n-dimensional sphere $S^n\simeq\SO(n+1)/\SO(n)$ and the spherical functions of the n-dimensional real projective space $P^n(\mathbb{R ...
Monotonicity of zeros of Laguerre-Sobolev-type orthogonal polynomials
(Academic Press Inc. Elsevier B.V., 2010-08-01)
Denote by x(n,k)(M,N)(alpha), k = 1, ..., n, the zeros of the Laguerre-Sobolev-type polynomials L(n)((alpha, M, N))(x) orthogonal with respect to the inner product< p, q > = 1/Gamma(alpha + 1) integral(infinity)(0)p(x)q( ...
Monotonicity of zeros of Laguerre-Sobolev-type orthogonal polynomials
(Academic Press Inc. Elsevier B.V., 2010-08-01)
Denote by x(n,k)(M,N)(alpha), k = 1, ..., n, the zeros of the Laguerre-Sobolev-type polynomials L(n)((alpha, M, N))(x) orthogonal with respect to the inner product< p, q > = 1/Gamma(alpha + 1) integral(infinity)(0)p(x)q( ...
Asymptotic Behavior and Zero Distribution of Polynomials Orthogonal with Respect to Bessel Functions
(Springer, 2016-02)
We consider polynomials Pn orthogonal with respect to the weight Jν on [0,∞), where Jν is the Bessel function of order ν. Asheim and Huybrechs considered these polynomials in connection with complex Gaussian quadrature for ...