Operator Theory
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Beschreibung
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.
Embraces the long history, diversity and wide range of topics relating to operator theory
Explores notions such as positivity and reproducing kernel through interconnected sections
Describes multiple applications and connections with other fields of mathematics, physics and Engineering
Provides a timely reference work on operator theory
Includes supplementary material: sn.pub/extras
Autor*in
Daniel Alpay
Themen in »Operator Theory«
Schur analysis de Branges spaces indefinite inner product spaces infinite dimensional analysis noncommutative analysis reproducing kernel Hilbert spaces