Date of Award
2022
Document Type
Thesis
Degree Name
Bachelors
Department
Natural Sciences
First Advisor
McDonald, Patrick
Area of Concentration
Mathematics with Spanish
Abstract
The first Dirichlet eigenvalue of the Laplace operator is a well known geometric in- variant, as is the volume of a domain. In 1951 Polya and Szego proved an inequality relating these to torsional rigidity, a geometric invariant related to the Laplace op- erator which arises in the theory of elastic bodies. Via the theory of Dirichlet forms we extend the Polya and Szego result to a class of self-adjoint operators associated to stochastic processes.
Recommended Citation
Hunter, Evan, "A GENERALIZATION OF POLYA’S INEQUALITY FOR TORSIONAL RIGIDITY AND PRINCIPAL FREQUENCY VIA THE THEORY OF DIRICHLET FORMS" (2022). Theses & ETDs. 6249.
https://digitalcommons.ncf.edu/theses_etds/6249