Linear Operators and their Spectra

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Focusing on the spectral theory of non-self-adjoint linear operators, this comprehensive text is tailored for postgraduate students and researchers. It covers essential topics such as Fredholm theory, Hilbert-Schmidt operators, and one-parameter semigroups, with applications to Markov semigroups. The book introduces the theory of pseudospectra and explores recent advancements in understanding their behavior related to orthogonal polynomials. Additionally, it presents innovative methods for estimating eigenvalues of non-self-adjoint Schrödinger operators and examines the unique spectral features of the non-self-adjoint harmonic oscillator.