作用素論ハンドブック（全２巻） Operator Theory〈1st ed. 2015〉

著者名：Alpay, Daniel (EDT)/Woracek, Harald (EDT)

Springer（2015/08/04発売）

• 言語：ENG
• ISBN：9783034806664
• eISBN：9783034806671

Description

A one-sentence definition of operator theory could be: The study of (linear) continuous operations between topological vector spaces, these being in general (but not exclusively) Fréchet, Banach, or Hilbert spaces (or their duals). Operator theory is thus a very wide field, with numerous facets, both applied and theoretical. There are deep connections with complex analysis, functional analysis, mathematical physics, and electrical engineering, to name a few. Fascinating new applications and directions regularly appear, such as operator spaces, free probability, and applications to Clifford analysis. In our choice of the sections, we tried to reflect this diversity. This is a dynamic ongoing project, and more sections are planned, to complete the picture. We hope you enjoy the reading, and profit from this endeavor.

Table of Contents

General aspects of quaternionic and Clifford analysis.- Further developments of quaternionic and Clifford analysis.- Infinite dimensional analysis.- Non-commutative theory.- Multivariable operator theory.- Reproducing kernel Hilbert spaces.- de Branges spaces.- Indefinite inner product spaces.- Schur analysis.- Linear system theory.