Schrödinger Operators, Markov Semigroups, Wavelet Analysis, Operator Algebras

The analysis of partial differential equations has stimulated large areas of research in mathematical physics, harmonic analysis, and operator theory. The present volume seeks to illuminate the depth and variety of these interactions. It begins with a survey on the use of semiclassical analysis and maximum-principle techniques in statistical mechanics. There follows an article presenting the perturbation theory for generators of Markov semigroups acting on Lp. The third contribution provides a self-contained introduction to continuous wavelet analysis, including its relations to function spaces and microlocal regularity; this should be of particular interest, as wavelet methods have been applied with great success in the 1990s to problems in harmonic and numerical analysis as well as in diverse fields of engineering. The final section explores pseudo-differential analysis on singular configurations, with special emphasis on C*-algebra techniques, Mellin operators, and analytical index formulas.