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SPECTRAL THEORY OF AUTOMORPHIC FUNCTIONS, THE SELBERG ZETA-FUNCTION, AND SOME PROBLEMS OF ANALYTIC NUMBER THEORY AND MATHEMATICAL PHYSICS

Russian Mathematical Surveys, 1979
CONTENTS § 0. Introduction Chapter I. Selberg theory on a compact Riemann surface § 1. The Voronoi-Hardy formula § 2. Elementary spectral theory of automorphic functions § 3. The Selberg trace formula § 4. The Selberg zeta-function § 5. Refinement of the spectral theory of automorphic functions § 6. The problem of moduli Chapter 2.
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Spectral Theory and Quantum Mechanics: Mathematical Foundations of Quantum Theories, Symmetries and Introduction to the Algebraic Formulation

2017
This book discusses the mathematical foundations of quantum theories. It offers an introductory text on linear functional analysis with a focus on Hilbert spaces, highlighting the spectral theory features that are relevant in physics. After exploring physical phenomenology, it then turns its attention to the formal and logical aspects of the theory ...
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Spectral expansions and excursion theory for non-self-adjoint Markov semigroups with applications in mathematical finance

2017
This dissertation consists of three parts. In the first part, we establish a spectral theory in the Hilbert space L2(R+) of the C0-semigroup P and its adjoint bP having as generator, respectively, the Caputo and the right-sided Riemann-Liouville fractional derivatives of index 1 < alpha < 2.
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