Operators in Hilbert Space, and their Applications (original) (raw)

2014, arXiv: Functional Analysis

Over the decades, Functional Analysis has been enriched and inspired on account of demands from neighboring fields, within mathematics, harmonic analysis (wavelets and signal processing), numerical analysis (finite element methods, discretization), PDEs (diffusion equations, scattering theory), representation theory; iterated function systems (fractals, Julia sets, chaotic dynamical systems), ergodic theory, operator algebras, and many more. And neighboring areas, probability/statistics (for example stochastic processes, Ito and Malliavin calculus), physics (representation of Lie groups, quantum field theory), and spectral theory for Schr\"odinger operators. We have strived for a more accessible book, and yet aimed squarely at applications; -- we have been serious about motivation: Rather than beginning with the four big theorems in Functional Analysis, our point of departure is an initial choice of topics from applications. And we have aimed for flexibility of use; acknowledgi...