Perturbation theory, M-essential spectra of operator matrices

Perturbation theory for Hamiltonian operator matrices and Riccati equations

Variational Perturbation Theory for Density Matrices

Variational perturbation theory [1,2] transforms divergent perturbation expansions into convergent ones. The convergence extends to infinitely strong couplings [3], a property which has recently been used to derive critical exponents in field theory without renormalization group methods [4,5]. The theory has first been developed in quantum mechanics for the path integral representation of the f...

Relative Perturbation Theory for Diagonally Dominant Matrices

OF DISSERTATION RELATIVE PERTURBATION THEORY FOR DIAGONALLY DOMINANT MATRICES Diagonally dominant matrices arise in many applications. In this work, we exploit the structure of diagonally dominant matrices to provide sharp entrywise relative perturbation bounds. We first generalize the results of Dopico and Koev to provide relative perturbation bounds for the LDU factorization with a well condi...

Perturbation of Essential Spectra of Exterior Elliptic Problems

For a second-order symmetric strongly elliptic differential operator on an exterior domain in Rn it is known from works of Birman and Solomiak that a change of the boundary condition from the Dirichlet condition to an elliptic Neumann or Robin condition leaves the essential spectrum unchanged, in such a way that the spectrum of the difference between the inverses satisfies a Weyl-type asymptoti...

Operator Theory - Spectra and Functional Calculi