Slice hyperholomorphic functions

Daniel Alpay, Fabrizio Colombo, Irene Sabadini

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review

43 Scopus citations


In the first section of this chapter we give a brief survey of the theory of slice hyperholomorphic functions, and we provide the basic results needed in the sequel. The theory is much more developed and we refer the reader to the Introduction to Part II of the present work for references. Then, the Sections from 6.2 to 6.5 focus on the functions slice hyperholomorphic in the unit ball. We define in particular the Hardy space of the ball, Schur functions, and Blaschke factors. We also study linear fractional transformations and introduce the Wiener algebra of the ball. The last two sections, 6.6 and 6.7, are devoted to the case of functions slice hyperholomorphic in the half-space of quaternions with real positive part. We discuss in particular the Hardy space and Blaschke factors.

Original languageEnglish
Title of host publicationOperator Theory
Subtitle of host publicationAdvances and Applications
PublisherSpringer International Publishing
Number of pages48
StatePublished - 1 Jan 2016
Externally publishedYes

Publication series

NameOperator Theory: Advances and Applications
ISSN (Print)0255-0156
ISSN (Electronic)2296-4878

ASJC Scopus subject areas

  • Analysis


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