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Spectral theory of block operator matrices and applications in mathematical physics

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Block operator matrices are matrices the entries of which are linear operators. They arise frequently in applications, e.g. when considering coupled systems of differential equations. In this talk we shall investigate the spectral theory of block operator matrices. Questions to be addressed include the location and structure of the spectrum and criteria for block diagonalization; the latter is closely related to the existence of solutions of algebraic Riccati equations. Applications to problems from hydrodynamics, magnetohydrodynamics, and quantum mechanics will be presented.

This talk is part of the Applied and Computational Analysis series.

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