Sergio Albeverio ist ein Schweizer Mathematiker und mathematischer Physiker, der für seine umfangreichen Beiträge in zahlreichen Bereichen der Mathematik und ihrer Anwendungen bekannt ist. Seine Arbeit umfasst Wahrscheinlichkeitstheorie, Analysis, mathematische Physik, Algebra, Geometrie und Zahlentheorie. Er initiierte gemeinsam mit Raphael Høegh-Krohn eine systematische mathematische Theorie der Feynman-Pfadintegrale und unendlich-dimensionaler Dirichlet-Formen. Darüber hinaus leistete er wesentliche Beiträge zur Entwicklung der p-adischen Funktional- und stochastischen Analysis und initiierte einen neuen Ansatz zur Untersuchung der Entstehung von Galaxien und Planeten, inspiriert von der stochastischen Mechanik.
Highlights the analysis on noncompact and singular manifolds within the framework of the cone calculus with asymptotics. This title deals with parabolic equations, a topic relevant for many applications. It presents a calculus for pseudodifferential operators with an anisotropic analytic parameter.
The Bulletin of the American Mathematical Society acclaimed this text as "a welcome addition" to the literature of nonstandard analysis, a field related to number theory, algebra, and topology. The first half presents a complete and self-contained introduction to the subject, and the second part explores applications to stochastic analysis and mathematical physics.The text's opening chapters introduce all of the material needed later, including a nonstandard development of the calculus, aspects of singular perturbation theory related to ordinary differential equations, and applications to topology and functional analysis. A significant portion of the text focuses on applications of nonstandard analysis to probability theory. Starting with nonstandard measure theory, the treatment advances to probability problems that can be represented by hyperfinite nonstandard models. Applications of nonstandard analysis to stochastic processes are treated at length, and the authors present numerous applications to mathematical physics. Additional topics include hyperfinite Dirichlet forms and Markov processes, differential operators, and hyperfinite lattice models.