The C-property for slice regular functions and applications to the Bergman space

Fabrizio Colombo, J. Oscar González-Cervantes, Irene Sabadini

Research output: Contribution to journalArticle

23 Citations (Scopus)

Abstract

This article has a twofold purpose: on one hand, we deepen the study of slice regular functions by studying their behaviour with respect to the so-called C-property and anti-C-property. We show that, for any fixed basis of the algebra of quaternions ℍ any slice regular function decomposes into the sum of four slice regular components, each of them satisfying the C-property. Then, we will use these results to show a reproducing property of the Bergman kernels of the second kind. © 2013 Copyright Taylor and Francis Group, LLC.
Original languageAmerican English
Pages (from-to)1355-1372
Number of pages1217
JournalComplex Variables and Elliptic Equations
DOIs
StatePublished - 1 Oct 2013
Externally publishedYes

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Bergman Space
Slice
Algebra
Bergman Kernel
Quaternion
Decompose

Cite this

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The C-property for slice regular functions and applications to the Bergman space. / Colombo, Fabrizio; González-Cervantes, J. Oscar; Sabadini, Irene.

In: Complex Variables and Elliptic Equations, 01.10.2013, p. 1355-1372.

Research output: Contribution to journalArticle

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