Polinômios de Szegö e análise de frequência

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Polinômios para-ortogonais e análise de freqüência

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Characterization theorem for classical orthogonal polynomials on non-uniform lattices: The functional approach

Using the functional approach, we state and prove a characterization theorem for classical orthogonal polynomials on non-uniform lattices (quadratic lattices of a discrete or a q-discrete variable) including the Askey-Wilson polynomials. This theorem proves the equivalence between seven characterization properties, namely the Pearson equation for the linear functional, the second-order divided-difference equation, the orthogonality of the derivatives, the Rodrigues formula, two types of structure relations,and the Riccati equation for the formal Stieltjes function.

BASIC HYPERGEOMETRIC FUNCTIONS and ORTHOGONAL LAURENT POLYNOMIALS

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Szego polynomials: some relations to L-orthogonal and orthogonal polynomials

We consider the real Szego polynomials and obtain some relations to certain self inversive orthogonal L-polynomials defined on the unit circle and corresponding symmetric orthogonal polynomials on real intervals. We also consider the polynomials obtained when the coefficients in the recurrence relations satisfied by the self inversive orthogonal L-polynomials are rotated. (C) 2002 Elsevier B.V. B.V. All rights reserved.

Riemann-Hilbert problems for poly-Hardy space on the unit ball

In this paper, we focus on a Riemann–Hilbert boundary value problem (BVP) with a constant coefficients for the poly-Hardy space on the real unit ball in higher dimensions. We first discuss the boundary behaviour of functions in the poly-Hardy class. Then we construct the Schwarz kernel and the higher order Schwarz operator to study Riemann–Hilbert BVPs over the unit ball for the poly- Hardy class. Finally, we obtain explicit integral expressions for their solutions. As a special case, monogenic signals as elements in the Hardy space over the unit sphere will be reconstructed in the case of boundary data given in terms of functions having values in a Clifford subalgebra. Such monogenic signals represent the generalization of analytic signals as elements of the Hardy space over the unit circle of the complex plane.

Reflecting on the ‘Dream Circle’ : urban Indigenous education processes designed for student and community empowerment

The ‘Dream Circle’ is a space designed by and operated through Indigenous educator footprints as a safe space for the school’s deadly jarjums (Indigenous children). The ‘Dream Circle’ uses a kinnected methodology drawing on the rich vein of Murri cultural knowledges and Torres Strait Islander supports within the local community to provide a safe and supportive circle. The ‘Dream Circle’ operates on a school site in the Logan area as an after school homework and cultural studies class. The ‘Dream Circle’ embodies practices and ritualises processes which ensure cultural safety and integrity. In this way the ‘Dream Circle’ balances the measures that Sarra (2005) purports are the stronger, smarter realities needed for positive change in Indigenous education.

Frame presentations: variants of the reals, rings of functions, their Dedekind completions, and the unit circle

176 p.

Feature tracking on the unit-sphere

Techniques used in a previous study of the objective identification and tracking of meteorological features in model data are extended to the unit sphere. An alternative feature detection scheme is described based on cubic interpolation for the sphere and local maximization. The extension of the tracking technique, used in the previous study, to the unit sphere is described. An example of the application of these techniques to a global relative vorticity field from a model integration are presented and discussed.

SYMMETRICAL ORTHOGONAL POLYNOMIALS AND THE ASSOCIATED ORTHOGONAL L-POLYNOMIALS

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 information regarding the orthogonal polynomials associated with the weight function (1 + kx(2))(1 - x(2))(-1/2), k > 0.

Polinômios ortogonais e análise de freqüência

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)