Michael Demuth Knihy

This volume presents self-contained survey articles on modern research areas written by experts in their fields. The topics are located at the interface of spectral theory, theory of partial differential operators, stochastic analysis, and mathematical physics. The articles are accessible to graduate students and researches from other fields of mathematics or physics while also being of value to experts, as they report on the state of the art in the respective fields.

This work explores various advanced topics in mathematical physics and operator theory, including the heat equation asymptotics of a generalized Ahlfors Laplacian on manifolds with boundaries and the contrasting behaviors of recurrent versus diffusive quantum systems under time-dependent Hamiltonians. It delves into spectral measures for Feller operators and provides a global perspective on locating quantum resonances. The text presents estimates for eigenvalues in elliptic problems and discusses quantum scattering in the presence of long-range magnetic fields. It addresses spectral invariance and submultiplicativity in Fréchet algebras, with applications to pseudo-differential operators and *-quantization. Key results include exponential decay of eigenfunctions for Kac's operator in higher dimensions and second-order perturbations of divergence-type operators exhibiting a spectral gap. The analysis extends to Weyl quantized relativistic Hamiltonians and spectral asymptotics for commuting operator families. Additionally, it examines pseudo-differential operators with negative definite symbols, one-dimensional Schrödinger operators with high barriers, and boundary value problems in angular domains. Insights into non-linear equations in cylindrical domains, stable asymptotics for Dirichlet problems, and Maslov operator calculus are also presented, alongside discussions on trace formulas and functional calculus for boundary value

This work focuses on various known criteria in the spectral theory of selfadjoint operators. The concise, unified presentation is aimed at graduate students and researchers working in the spectral theory of Schrodinger operators with either fixed or random potentials. But given the large gap this book fills in the literature, it will serve a wider audience of mathematical physicists in its contribution to works in spectral theory.

„Das Bundesverfassungsgericht und die Mitbestimmung im öffentlichen Dienst“ Am 24.05.95 hat das Bundesverfassungsgericht im Rahmen einer abstrakten Normenkontrolle über die Verfassungsmäßigkeit des schleswig-holsteinischen Mitbestimmungsgesetzes entschieden. Dieses Gesetz war Gegenstand heftiger politischer und juristischer Kontroversen. Das lag zum einen an der Bedeutung der Frage, die mit der Mitbestimmung abhängig Beschäftigter verbunden sind, zum anderen an den Antworten, die das schleswig-holsteinische Mitbestimmungsgesetz darauf gegeben hat. Gegenstand dieser Dissertation ist es, die Auswirkungen dieser Entscheidung deutlich zu machen.

The intention of the international conference PDE2000 was to bring together specialists from different areas of modern analysis, mathematical physics and geometry, to discuss not only the recent progress in their own fields but also the interaction between these fields. The special topics of the conference were spectral and scattering theory, semiclassical and asymptotic analysis, pseudodifferential operators and their relation to geometry, as well as partial differential operators and their connection to stochastic analysis and to the theory of semigroups. The scientific advisory board of the conference in Clausthal consisted of M. Ben-Artzi (Jerusalem), Chen Hua (Peking), M. Demuth (Clausthal), T. Ichinose (Kanazawa), L. Rodino (Turin), B.-W. Schulze (Potsdam) and J. Sjöstrand (Paris). The book is aimed at researchers in mathematics and mathematical physics with interests in partial differential equations and all its related fields.

A beautiful interplay between probability theory (Markov processes, martingale theory) on the one hand and operator and spectral theory on the other yields a uniform treatment of several kinds of Hamiltonians such as the Laplace operator, relativistic Hamiltonian, Laplace-Beltrami operator, and generators of Ornstein-Uhlenbeck processes. For such operators regular and singular perturbations of order zero and their spectral properties are investigated. A complete treatment of the Feynman-Kac formula is given. The theory is applied to such topics as compactness or trace class properties of differences of Feynman-Kac semigroups, preservation of absolutely continuous and/or essential spectra and completeness of scattering systems. The unified approach provides a new viewpoint of and a deeper insight into the subject. The book is aimed at advanced students and researchers in mathematical physics and mathematics with an interest in quantum physics, scattering theory, heat equation, operator theory, probability theory and spectral theory.

Evolution equations describe many processes in science and engineering, and they form a central topic in mathematics. The first three contributions to this volume address parabolic evolutionary The opening paper treats asymptotic solutions to singular parabolic problems with distribution and hyperfunction data.The theory of the asymptotic Laplace transform is developed in the second paper and is applied to semigroups generated by operators with large growth of the resolvent. An article follows on solutions by local operator methods of time-dependent singular problems in non-cylindrical domains.The next contribution addresses spectral properties of systems of pseudodifferential operators when the characteristic variety has a conical intersection. Bohr-Sommerfeld quantization rules and first order exponential asymptotics of the resonance widths are established under various semiclassical regimes.In the following article, the limiting absorption principle is proven for certain self-adjoint operators. Applications include Hamiltonians with magnetic fields, Dirac Hamiltonians, and the propagation of waves in inhomogeneous media.The final topic develops Hodge theory on manifolds with edges; its authors introduce a concept of elliptic complexes, prove a Hodge decomposition theorem, and study the asymptotics of harmonic forms.

Part of a series originating from the work of the Max Planck Research Group for Partial Differential Equations and Complex Analysis at the University of Potsdam, Germany. The text seeks to promote expositions of a systematic character in the field of partial differential equations.