Analytic Methods Of Spectral Representations Of Nonselfadjoint Nonunitary Operators Jeanmichel Morel by Jean-michel Morel, City University Of Hong Kong, Kowloon Tong, Chinabernard Teissier, Imj-prg, Paris, France 9783031716560, 9783031716577, 3031716566, 3031716574 instant download after payment.

The rapid advancement of quantum mechanics at the start of the twentieth centuryinitiated the development of the mathematical apparatus that lies at the basis ofquantum theory. J. von Neumann, in his 1932 book Mathematische Grunlagen derQuantenmechanik, was the first to give quantum mechanics its logically consistentform, stating it as a unified theory which is based on the spectral theory of selfadjoint operators acting on Hilbert spaces. The further development of Hilbert spacetheory and operator theory lies at the basis of an elegant theory, functional analysis.In each concrete situation, the general principles of functional analysis naturallyhave individual features which sometimes lead to the formation of a deep theory.Thus, the spectral analysis of self-adjoint Sturm–Liouville operators has been asource of numerous studies and applications for more than two centuries. Resultsfor self-adjoint, unitary, and normal operators acting on Hilbert spaces form thenon-trivial constructive apparatus of many mathematical theories.Numerous attempts to construct spectral expansions for non-self-adjoint operators, analogous to the self-adjoint case, have met with significant difficulties. Historically, the Riesz contour integral of the resolvent is the first general method ofspectral analysis for non-self-adjoint operators. However, serious analytic difficulties arising in the estimation of the resolvent on series of contours dividing thespectrum (e.g., for the Schrödinger non-self-adjoint operator) became the mainreason for the non-efficiency of this approach. Moreover, constructions of spectralexpansions for concrete non-self-adjoint differential operators in the same form asfor self-adjoint ones showed that the spectral function is a distribution, and this notonly narrowed the class of such operators but created certain analytical difficulties.Thus, the insufficiency of an analytic base of spectral analysis brings forward theproblem of construction of principally new