Particle Spreading in a Simple Majda Flow and Eigenvalue Estimation Through a Cayley Transform

The spectrum of the integral operator whose kernel is the covariance function of a random variable plays an important role in finding the distribution of the random variable. We consider methods for producing estimates of the eigenvalues of such operators. If such an operator can be written in the form H0 + H1 with H 1 relatively compact to H0, then the eigenvalues are asymptotically close to those of H0. This method does not, however, produce good error estimates. We consider a perturbation method based on a Cayley transform. We show that the change of basis V = (I + K/2)-1( I - K/2), where I is the identity operator and K is a skew-adjoint operator given by a formal perturbation argument, gives better error estimate.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2015

Author dc:creator

• Lee, Jae-Ug

Contributors dc:contributor

• Bronski, Jared C.

• Mathematics

Language dc:language

eng

Identifier

(MiAaPQ)AAI3250276

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/86876