4 papers · 1 filter
Orthogonality, Spectral Filling, and Uncertainty
Travis Alvarez, Trevor Camper, Mishko Mitkovski
Let a normalized continuous Parseval frame describe the phase space of a reproducing kernel Hilbert space. The frame coefficients of an orthonormal family have total mass equal to…
Nonexistence of Approximately Dual Frames via Weighted Composition Operators
Trevor Camper, Dongwei Chen, Shuang Guan
Reconstruction from the coefficients of a frame often requires a dual frame, and the canonical dual is obtained by inverting the frame operator, which is rarely available in a clos…
A Szegő Limit Theorem for Radially-Compressed Toeplitz Operators
Trevor Camper
We obtain Szegő-type Limit Theorems in the setting of Reproducing Kernel Hilbert Spaces on discs in . From this, we derive a formula for the density of the eigenvalues…
A Semi-Classical Szegő-type Limit Theorem for Toeplitz Operators
Trevor Camper, Mishko Mitkovski
We establish an abstract Szegő-type limit theorem for Toeplitz operators associated with normalized continuous Parseval frames. Our assumptions consist essentially of a natural nor…