Slice hyperholomorphic Schur analysis

Daniel Alpay, Fabrizio Colombo, Irene Sabadini

Research output: Book/ReportBookpeer-review


This book defines and examines the counterpart of Schur functions and Schur analysis in the slice hyperholomorphic setting. It is organized into three parts: the first introduces readers to classical Schur analysis, while the second offers background material on quaternions, slice hyperholomorphic functions, and quaternionic functional analysis. The third part represents the core of the book and explores quaternionic Schur analysis and its various applications. The book includes previously unpublished results and provides the basis for new directions of research.
Original languageEnglish
Place of PublicationCham, Switzerland
Number of pages362
Edition1st ed. 2016
ISBN (Electronic)3319425145, 9783319425146
ISBN (Print)9783319425139
StatePublished - 2016

Publication series

NameOperator Theory: Advances and Applications
PublisherSpringer International Publishing; Imprint: Birkhäuser


  • Slice hyperholomorphic functions
  • quaternions
  • reproducing kernels
  • reproducing kernel spaces
  • analytic functions
  • linear operators
  • linear systems
  • interpolation problems
  • indefinite inner product spaces
  • Krein and Pontryagin spaces


Dive into the research topics of 'Slice hyperholomorphic Schur analysis'. Together they form a unique fingerprint.

Cite this