Wick ordering of creation and annihilation operators is of fundamental importance for computing averages and correlations in quantum field theory and, by extension, in the Hudson-Parthasarathy theory of quantum stochastic processes, quantum mechanics, stochastic processes, and probability. This book develops the unified combinatorial framework behind these examples, starting with the simplest mathematically, and working up to the Fock space setting for quantum fields. Emphasizing ideas from combinatorics such as the role of lattice of partitions for multiple stochastic integrals by...

This first volume of a two-volume overview covers the basic theory of Banach spaces, harmonic analysis and probability.

This second volume of a two-volume overview focuses on the applications of Banach spaces and recent developments in the field.

A self-contained introduction to discrete harmonic analysis with an emphasis on the Discrete and Fast Fourier Transforms.

A self-contained introduction to the analytical aspects of automorphic forms, with key proofs of critical results and extensive examples.

Detailed exposition of automorphic representations and their relation to string theory, for mathematicians and theoretical physicists.

A self-contained introduction to logarithmic geometry, a key tool for analyzing compactification and degeneration in algebraic geometry.