Shrodinger Operators, Markov Semigroups, Wavelet Analysis, Operator Algebras

This volume illuminates the depth and variety of analysis of partial differential equations. It begins with a survey on the use of semi-classical analysis and operator theory, before going on to present the perturbation theory for generators of Markov semigroups acting on Lp. The third section provides a self-contained introduction to continuous wavelet analysis, including its relations to function spaces and microlocal regularity. Finally, the text explores pseudo-differential analysis on singular configurations, with special emphasis on C-algebra techniques, Merlin operators, and analytical index formulas.