MODELS ELECTROSTATICOS OF ZEROS OF POLYNOMIALS SEMICLASICOSAuthor:
GARRIDO BERENGUEL ANGELES.
Year:
2004.
University:
CARLOS III DE MADRID [
www.uc3m.es].
Place of defense: ESCUELA POLITECNICA SUPERIOR.
Place of preparation: UNIVERSIDAD CARLOS III DE MADRID.
Summary: In this report we studied and developed a mathematical model for the treatment of electrostatic distribution of zeros of polynomials orthogonal regard to functional semiclásicos. These functional satisfy a differential equation distribucional Pearson. These functional cover a wide range of examples that appear in numerous models of mathematical physics, statistics, etc.. The results obtained in this report in a generic context have been analyzed in detail in a number of models not treated so far and that illuminate the power of the techniques used. We have also compared different methodologies to address the problem of electrostatic distribution of zeros, that is, both from a perspective of the theory of potential to another oriented structural properties of orthogonal polynomials. It introduces the concept of a class of functional semiclásico and discusses the kind of a family of functional disturbance of classics by adding a finite amount of resulting mass Dirac located on the border of support far orthogonality. It also introduces the process simetrización to study the class of functional simetrizados of functional semiclásicos. It deals with the interpretation of electrostatic zeros of polynomials orthogonal subsequently analyzing the case of the weights of Freud as a model semiclásico type Hermite. Finally analyzes the structural properties of orthogonal polynomials respect to a linear functional type Freud and presents the interpretation electrostatic the distribution of zeros.
