Analysis Seminar: Operator compactness via almost diagonalization
Speaker: Cody Stockdale, Clemson University
Abstract: We discuss a general philosophy that loosely states that if the matrix representation of a linear operator is concentrated on its diagonal, then the operator’s compactness is characterized by the decay of its matrix representation along the diagonal. We formulate rigorous versions of this idea in abstract settings and apply them to study the compactness of Calderón-Zygmund operators, pseudodifferential operators, and Fourier integral operators. These applications recover and unify various earlier works and provide new results.
Host: Brandon Sweeting