On computational aspects of discrete Sobolev inner products on the unit circle

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 component involving derivatives is located outside the closed unit disk. As a consequence, we deduce the outer relative asymptotics of these polynomials in terms of those associated with the original orthogonality measure. Moreover, we show how to recover the discrete part of our Sobolev inner product. © 2013 Elsevier Inc. All rights reserved.

Análise funcional e aplicações

Pós-graduação em Matemática Universitária - IGCE

Polinômios ortogonais de Laurent na reta real e no círculo unitário

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Analogia entre propriedades de alguns polinômios ortogonais em uma e em várias variáveis

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Continuous vs. segmented second-dimension system gradients for comprehensive two-dimensional liquid chromatography of sugarcane (Saccharum spp.)

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Analytical solution for transient one-dimensional couette flow considering constant and time-dependent pressure gradients

This paperaims to determine the velocity profile, in transient state, for a parallel incompressible flow known as Couette flow. The Navier-Stokes equations were applied upon this flow. Analytical solutions, based in Fourier series and integral transforms, were obtained for the one-dimensional transient Couette flow, taking into account constant and time-dependent pressure gradients acting on the fluid since the same instant when the plate starts it´s movement. Taking advantage of the orthogonality and superposition properties solutions were foundfor both considered cases. Considering a time-dependent pressure gradient, it was found a general solution for the Couette flow for a particular time function. It was found that the solution for a time-dependent pressure gradient includes the solutions for a zero pressure gradient and for a constant pressure gradient.