Interpolation with symmetry and a Herglotz theorem in the bicomplex setting

Daniel Alpay; Izchak Lewkowicz; Mihaela Vajiac

doi:10.1016/j.jmaa.2023.127201

Interpolation with symmetry and a Herglotz theorem in the bicomplex setting

Daniel Alpay, Izchak Lewkowicz, Mihaela Vajiac

Department of Electrical & Computer Engineering

Research output: Contribution to journal › Article › peer-review

Abstract

We present a new approach to Schur analysis in the bicomplex setting, reducing the various underlying questions to interpolation problems in the complex setting with an appropriate symmetry condition.

Original language	English
Article number	127201
Journal	Journal of Mathematical Analysis and Applications
Volume	524
Issue number	2
DOIs	https://doi.org/10.1016/j.jmaa.2023.127201
State	Published - 15 Aug 2023

Keywords

Bi-tangential interpolation
Bicomplex analysis
Carathéodory functions
Positive functions
Two-sided interpolation

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1016/j.jmaa.2023.127201

Cite this

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title = "Interpolation with symmetry and a Herglotz theorem in the bicomplex setting",

abstract = "We present a new approach to Schur analysis in the bicomplex setting, reducing the various underlying questions to interpolation problems in the complex setting with an appropriate symmetry condition.",

keywords = "Bi-tangential interpolation, Bicomplex analysis, Carath{\'e}odory functions, Positive functions, Two-sided interpolation",

author = "Daniel Alpay and Izchak Lewkowicz and Mihaela Vajiac",

note = "Funding Information: D. Alpay thanks the Foster G. and Mary McGaw Professorship in Mathematical Sciences, which supported his research. All authors thank the anonymous reviewers for their care and attention to our work. Publisher Copyright: {\textcopyright} 2023 Elsevier Inc.",

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AU - Alpay, Daniel

AU - Lewkowicz, Izchak

AU - Vajiac, Mihaela

N1 - Funding Information: D. Alpay thanks the Foster G. and Mary McGaw Professorship in Mathematical Sciences, which supported his research. All authors thank the anonymous reviewers for their care and attention to our work. Publisher Copyright: © 2023 Elsevier Inc.

PY - 2023/8/15

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AB - We present a new approach to Schur analysis in the bicomplex setting, reducing the various underlying questions to interpolation problems in the complex setting with an appropriate symmetry condition.

KW - Bi-tangential interpolation

KW - Bicomplex analysis

KW - Carathéodory functions

KW - Positive functions

KW - Two-sided interpolation

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M3 - Article

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SN - 0022-247X

VL - 524

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ER -

Interpolation with symmetry and a Herglotz theorem in the bicomplex setting

Abstract

Keywords

ASJC Scopus subject areas

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