Manuscript received October 1, 1976; revised February 16, 1978. The author is with the Mathematical Institute, Oxford University, Oxford, England. [2], [13]. In the information-theoretic problem, theâ€¦ (More)

connections between integral kernels of positivity preserving semigroups and suitable Lp contractivity properties are established. Then these questions are studied for the semigroups generated by -Aâ€¦ (More)

A large font version of this manuscript is available. Please specify the font size that you need using Latex notation. I would welcome any information about errors in the text, to be sent to theâ€¦ (More)

We discuss the existence and completeness of scattering for onedimensional systems with different spatial asymptotics at Â± oo, for example 2 4V(x) where V(x) = 0 (resp. sin x) if x < 0 (resp. x > 0).â€¦ (More)

We give a mathematically rigorous analysis which confirms the surprising results in a recent paper [4] of Benilov, Oâ€™Brien and Sazonov about the spectrum of a highly singular non-self-adjointâ€¦ (More)

We obtain bounds on the complex eigenvalues of non-self-adjoint SchrÃ¶dinger operators with complex potentials, and also on the complex resonances of self-adjoint SchrÃ¶dinger operators. Our bounds areâ€¦ (More)

We study the pseudospectral theory of a variety of non-self-adjoint constant coeecient and variable coeecient diierential operators, showing that the phenomenon of non-trivial pseudospectra isâ€¦ (More)

We prove that the spectrum of certain non-self-adjoint SchrÃ¶dinger operators is unstable in the semi-classical limit h â†’ 0. Similar results hold for a fixed operator in the high energy limit. Theâ€¦ (More)

We prove sharp L 2 boundary decay estimates for the eigenfunctions of certain second order elliptic operators acting in a bounded region, and of their first space derivatives, using only the Hardyâ€¦ (More)