On a Nonself Adjoint Eigenfunction Expansion

Nonself-adjoint operator algebras for dynamical systems

This paper is a survey of our recent work on operator algebras associated to dynamical systems that lead to classification results for the systems in terms of algebraic invariants of the operator algebras.

On Eigenfunction Approximations for Typical Non-self-adjoint Schrödinger Operators

We construct efficient approximations for the eigenfunctions of non-selfadjoint Schrödinger operators in one dimension. The same ideas also apply to the study of resonances of self-adjoint Schrödinger operators which have dilation analytic potentials. In spite of the fact that such eigenfunctions can have surprisingly complicated structures with multiple local maxima, we show that a suitable ad...

Pricing Options on Scalar Diffusions: An Eigenfunction Expansion Approach

This paper develops an eigenfunction expansion approach to pricing options on scalar diffusion processes. All derivative securities are unbundled into portfolios of primitive securities termed eigensecurities. Eigensecurities are eigenvectors of the pricing operator (present value operator). Pricing is then immediate by the linearity property of the pricing operator and the eigenvector property...

Topics in the Theory of Nonself-adjoint Operator Algebras

Trotter Product Formula for Nonself-adjoint Gibbs Semigroups

We prove the trace-norm convergence of the Trotter product formula for nonself-adjoint Gibbs semigroups. For any m-sectorial generators A and B such that e ?tRe A is in the trace-class for t > 0, the Trotter product formula converges in the trace-norm. With smallness conditions on B with respect to A, we give error bound estimates of the convergence rate in this topology.