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On computational aspects of discrete Sobolev inner products on the unit circle
(2013-09-17)
In this paper, we show how to compute in O(n2) steps the Fourier coefficients associated with the Gelfand-Levitan approach for discrete Sobolev orthogonal polynomials on the unit circle when the support of the discrete ...
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 ...
On Newton-Sobolev spaces
(Kossuth Lajos Tudomanyegyetem, 2017-01)
Newton-Sobolev spaces, as presented by N. Shanmugalingam, describe a way to extend Sobolev spaces to the metric setting via upper gradients, for metric spaces with ´sucient´ paths of nite length. Sometimes, as is the case ...
Zeros of Jacobi-Sobolev orthogonal polynomials following non-coherent pair of measures
(2010-12-14)
Zeros of orthogonal polynomials associated with two different Sobolev inner products involving the Jacobi measure are studied. In particular, each of these Sobolev inner products involves a pair of closely related Jacobi ...
Zeros of Gegenbauer-Sobolev Orthogonal Polynomials: Beyond Coherent Pairs
(Springer, 2009-01-01)
Iserles et al. (J. Approx. Theory 65: 151-175, 1991) introduced the concepts of coherent pairs and symmetrically coherent pairs of measures with the aim of obtaining Sobolev inner products with their respective orthogonal ...
On a class of quasilinear elliptic problems involving critical exponents
(World Scientific Publ Co Pte LtdSingaporeSingapura, 2000)
Asymptotics for Gegenbauer-Sobolev orthogonal polynomials associated with non-coherent pairs of measures
(IOS Press, 2008-01-01)
Inner products of the type < f, g >(S) = < f, g >psi(0) + < f', g'>psi(1), where one of the measures psi(0) or psi(1) is the measure associated with the Gegenbauer polynomials, are usually referred to as Gegenbauer-Sobolev ...
A class of Sobolev orthogonal polynomials on the unit circle and associated continuous dual Hahn polynomials: Bounds, asymptotics and zeros
(2021-08-01)
This paper deals with orthogonal polynomials and associated connection coefficients with respect to a class of Sobolev inner products on the unit circle. Under certain conditions on the parameters in the inner product it ...
Fractional Sobolev spaces with variable exponents and fractional p(X)-Laplacians
(Univ Szeged, 2017-11)
In this article we extend the Sobolev spaces with variable exponents to include the fractional case, and we prove a compact embedding theorem of these spaces into variable exponent Lebesgue spaces. As an application we ...
On the Sobolev trace Theorem for variable exponent spaces in the critical range
(Springer Heidelberg, 2013-05)
In this paper, we study the Sobolev trace Theorem for variable exponent spaces with critical exponents. We find conditions on the best constant in order to guaranty the existence of extremals. Then, we give local conditions ...