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Multivariate sobolev-type orthogonal polynomials
(2011-12-01)
Multivariate orthogonal polynomials associated with a Sobolev-type inner product, that is, an inner product defined by adding to a measure the evaluation of the gradients in a fixed point, are studied. Orthogonal polynomials ...
Kernel polynomials from L-orthogonal polynomials
(2011-05-01)
A positive measure ψ defined on [a,b] such that its moments μn=∫a btndψ(t) exist for n=0,±1,±2,⋯, is called a strong positive measure on [a,b]. If 0≤a<b≤∞ then the sequence of (monic) polynomials {Qn}, defined by ∫a ...
New steps on Sobolev orthogonality in two variables
(Elsevier B.V., 2010-12-15)
Sobolev orthogonal polynomials in two variables are defined via inner products involving gradients. Such a kind of inner product appears in connection with several physical and technical problems. Matrix second-order partial ...
Perturbations on the antidiagonals of Hankel matrices
(2013-08-12)
Given a strongly regular Hankel matrix, and its associated sequence of moments which defines a quasi-definite moment linear functional, we study the perturbation of a fixed moment, i.e., a perturbation of one antidiagonal ...
BASIC HYPERGEOMETRIC FUNCTIONS and ORTHOGONAL LAURENT POLYNOMIALS
(Amer Mathematical Soc, 2012-06-01)
A three-complex-parameter class of orthogonal Laurent polynomials on the unit circle associated with basic hypergeometric or q-hypergeometric functions is considered. To be precise, we consider the orthogonality properties ...
SYMMETRICAL ORTHOGONAL POLYNOMIALS AND THE ASSOCIATED ORTHOGONAL L-POLYNOMIALS
(Amer Mathematical Soc, 1995-10-01)
We show how symmetric orthogonal polynomials can be linked to polynomials associated with certain orthogonal L-polynomials. We provide some examples to illustrate the results obtained Finally as an application, we derive ...
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 ...
Szego type polynomials and para-orthogonal polynomials
(Academic Press Inc. Elsevier B.V., 2010-10-01)
Szego type polynomials with respect to a linear functional M for which the moments M[t(n)] = mu(-n) are all complex, mu(-n) = mu(n) and D(n) not equal 0 for n >= 0. are considered. Here, D(n) are the associated Toeplitz ...
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( ...
Orthogonal polynomials on the unit circle and chain sequences
(2013-09-01)
Szego{double acute} has shown that real orthogonal polynomials on the unit circle can be mapped to orthogonal polynomials on the interval [-1,1] by the transformation 2x=z+z-1. In the 80's and 90's Delsarte and Genin showed ...