Division of distributions

• Grant number: 06/53020-5
• Support Opportunities: Scholarships in Brazil - Master
• Start date: September 01, 2006
• End date: August 31, 2008
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Paulo Domingos Cordaro
• Grantee: Mariana Smit Vega Garcia
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil

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 utilized in the general case. Ali the prerequisites for Hörmander's proof (the Theorems of Seidenberg-Tarski, of Puiseaux and Whitney's Extension Theorem) are discussed in detail. As a consequence of this theorem, it follows that every non zero partial differencial operator with constant coefficients has a tempered fundamental solution. (AU)

Academic Publications

(References retrieved automatically from State of São Paulo Research Institutions)

GARCIA, Mariana Smit Vega. Division of tempered distributions by polynomials.. 2008. Master's Dissertation - Universidade de São Paulo (USP). Instituto de Matemática e Estatística (IME/SBI) São Paulo.