Pseudo-Differential Operators, Generalized Functions and Asymptotics [Hardcover]

This volume consists of twenty peer-reviewed papers from the special session on pseudodifferential operators and the special session on generalized functions and asymptotics at the Eighth Congress of ISAAC held at the Peoples Friendship University of Russia in Moscow on August 2227, 2011. The category of papers on pseudo-differential operators contains such topics as elliptic operators assigned to diffeomorphisms of smooth manifolds, analysis on singular manifolds with edges, heat kernels and Green functions of sub-Laplacians on the Heisenberg group and Lie groups with more complexities than but closely related to the Heisenberg group, Lp-boundedness of pseudo-differential operators on the torus, and pseudo-differential operators related to time-frequency analysis. The second group of papers contains various classes of distributions and algebras of generalized functions with applications in linear and nonlinear differential equations, initial value problems and boundary value problems, stochastic and Malliavin-type differential equations. This second group of papers are related to the third collection of papers via the setting of Colombeau-type spaces and algebras in which microlocal analysis is developed by means of techniques in asymptotics. The volume?contains the synergies of the three areas treated?and is a useful complement to?volumes 155, 164, 172, 189, 205 and 213 published in the same series in, respectively, 2004, 2006, 2007, 2009, 2010 and 2011. ?Preface.- Elliptic Theory for Operators Associated with Diffeomorphisms of Smooth Manifolds.- The Singular Functions of Branching Edge Asymptotics.- The Heat Kernel and Green Function of the Sub-Laplacian on the Heisenberg Group.- Metaplectic Equivalence of the Hierarchical Twisted Laplacian.- The Heat Kernel and Green Function of a Sub-Laplacian on the Hierarchical Heisenberg Group.- Lp-Bounds for Pseudo-Differential Operators on the Torus.- Multiplication Properties in Gelfand-Shilov Pseudo-Differential Calculă+