Dr Petr Siegl - Advances in Spectral Theory for Non-Selfadjoint Operators

IAS Visiting Fellow Dr Petr Siegl delivers a seminar on their research - Many physical systems can be described by partial differential equations which in turn generate operators between Banach spaces. A well-known illustration of such interplay is quantum mechanics together with the spectral theory of self-adjoint operators in a Hilbert space. However, in several branches of physics like hydrodynamics, damped systems, quantum resonances, superconductivity or balanced loss/gain materials, the occurring PDEs contain non-symmetric terms and thus lead to non-self-adjoint operators. Due to the lack of powerful self-adjoint tools like the spectral theorem or variational principles, the encountered phenomena are very different from the self-adjoint case and include spectral instabilities, divergence of expansions in eigenvectors or non-reliability of approximations. In the first part of the talk, we give an introduction in the non-self-adjoint aspects of spectral theory. In the second part, we present new results on the convergence of the expansions in eigenvectors based on the local form subordination. For more information about the IAS, please visit - https://www.lboro.ac.uk/research/ias #maths #mathematics