D. Alpay (ed.): Operator Theory

Operator Theory, Editors: Daniel Alpay, Springer, Basel, 2015, ISBN: 978-3-0348-0666-4 (Print) 978-3-0348-0667-1 (Online)

About: 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.

The work contains a.o. the following two parts:

  • General Aspects of Quaternionic and Clifford Analysis
  • Further Developments of Quaternionic and Clifford Analysis

These two parts have the content:

Introductory Clifford Analysis
Sommen, Frank (et al.)
Pages 1339-1367

Quaternionic Analysis: Application to Boundary Value Problems
Gürlebeck, Klaus (et al.)
Pages 1369-1391

Function Spaces in Quaternionic and Clifford Analysis
Martin, Mircea
Pages 1393-1422

Quaternionic Analysis and Some Conventional Theories
Shapiro, Michael
Pages 1423-1446

Quaternionic and Clifford Analysis for Non-smooth Domains
Abreu-Blaya, Ricardo (et al.)
Pages 1447-1470

Clifford Analysis for Higher Spin Operators
Eelbode, David
Pages 1471-1490

Fueter Mapping Theorem in Hypercomplex Analysis
Qian, Tao
Pages 1491-1507

Representation Theory in Clifford Analysis
Souček, Vladimír
Pages 1509-1547

Quaternionic and Clifford Analysis in Several Variables
Struppa, Daniele C.
Pages 1549-1578

Hermitian Clifford Analysis
Sabadini, Irene (et al.)
Pages 1581-1608

Discrete Clifford Analysis
Kähler, Uwe (et al.)
Pages 1609-1630

Slice Hyperholomorphic Functions with Values in Some Real Algebras
Struppa, Daniele C.
Pages 1631-1650

Fourier Transforms in Clifford Analysis
Bie, Hendrik De
Pages 1651-1672

Wavelets in Clifford Analysis
Bernstein, Swanhild
Pages 1673-1699

Monogenic Signal Theory
Cerejeiras, Paula (et al.)
Pages 1701-1724

Some Peculiarities of Quaternionic Linear Spaces
Luna-Elizarrarás, Maria Elena (et al.)
Pages 1725-1743

Schur Analysis in the Quaternionic Setting: The Fueter Regular and the Slice Regular Case
Alpay, Daniel (et al.)
Pages 1745-1786

Slice Hyperholomorphic Functional Calculi
Colombo, Fabrizio (et al.)
Pages 1787-1821

The Monogenic Functional Calculus
Jefferies, Brian
Pages 1823-1851

Source: Email from springer@sci.scientific-direct.net, 6 Oct. 2015, http://link.springer.com/referencework/10.1007/978-3-0348-0667-1/page/1

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