Division of tempered distributions by polynomials.

Author(s)

Mariana Smit Vega Garcia

• Document type: Master's Dissertation
• Press: São Paulo.
• Institution: Universidade de São Paulo (USP). Instituto de Matemática e Estatística (IME/SBI)
• Defense date: 2008-08-29

Examining board members

Paulo Domingos Cordaro; Gerson Petronilho; Jorge Manuel Sotomayor Tello

• Advisor: Paulo Domingos Cordaro

Abstract

This dissertation presents a thorough proof of L. Hörmander\'s theorem on the division of (tempered) distributions by polynomials. The case n=1 is discussed in detail and serves as a motivation for the techniques that are utilised in the general case. All the prerequisites for Hörmander\'s proof (the Theorems of Seidenberg-Tarski, of Puiseux and Whitney\'s Extension Theorem) are discussed in detail. As a consequence of this theorem, it follows that every non zero partial diffe\\-rencial operator with constant coefficients has a tempered fundamental solution. (AU)

• FAPESP's process: 06/53020-5 - Division of distributions
• Grantee: Mariana Smit Vega Garcia
• Support Opportunities: Scholarships in Brazil - Master