Analysis of Pseudo-Differential Operators

This volume, like its predecessors, is based on the special session on pseudo-differential operators, one of the many special sessions at the 11th ISAAC Congress, held at Linnaeus University in Sweden on August 14-18, 2017. It includes research papers presented at the session and invited papers by experts in fields that involve pseudo-differential operators.The first four chapters focus on the functional analysis of pseudo-differential operators on a spectrum of settings from Z to Rn to compact groups. Chapters 5 and 6 discuss operators on Lie groups and manifolds with edge, while the following two chapters cover topics related to probabilities. The final chapters then address topics in differential equations.

Discrete Analogs of Wigner Transforms and Weyl Transforms.- Characterization of Non-Smooth Pseudodifferential Operators with Hölder Continuous Coefficients.- Fredholmness and Ellipticity of psi DOs on Bs pq(Rn) and Fspq(Rn).- Characterizations of Self-Adjointness, Normality, Invertibility and Unitarity of Pseudo-Differential Operators on Compact and Hausdorff Groups.- Multilinear Commutators in Variable Lebesgue Spaces on Stratied Groups.- Volterra Operators with Asymptotes on Manifolds with Edge.- Bismuts Way of the Malliavin Calculus for Non-Markovian Semi-Groups: an Introduction.- Operator Transformation of Probability Densities.- The Time-Frequency Interference Terms of the Greens Function for the Harmonic Oscillator.- On the Solvability in the Sense of Sequences for Some Non-Fredholm Operators Related to the Anomalous Diffusion.