Boundary Interpolation for Slice Hyperholomorphic Schur Functions

Khaled Abu-Ghanem; Daniel Alpay; Fabrizio Colombo; David P. Kimsey; Irene Sabadini

doi:10.1007/s00020-014-2184-3

Boundary Interpolation for Slice Hyperholomorphic Schur Functions

Khaled Abu-Ghanem, Daniel Alpay, Fabrizio Colombo, David P. Kimsey, Irene Sabadini

Department of Mathematics

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

9 Scopus citations

Abstract

A boundary Nevanlinna–Pick interpolation problem is posed and solved in the quaternionic setting. Given nonnegative real numbers (Formula presenred.), quaternions p₁,…,p_N all of modulus 1, so that the 2-spheres determined by each point do not intersect and p_u ≠ 1 for u = 1,…, N, and quaternions s₁,…, s_N, we wish to find a slice hyperholomorphic Schur function s so that(Formula presenred.).(Formula presenred.).Our arguments rely on the theory of slice hyperholomorphic functions and reproducing kernel Hilbert spaces.

Original language	English
Pages (from-to)	223-248
Number of pages	26
Journal	Integral Equations and Operator Theory
Volume	82
Issue number	2
DOIs	https://doi.org/10.1007/s00020-014-2184-3
State	Published - 1 Jun 2015

Keywords

30E05
30G35
47B32

ASJC Scopus subject areas

Analysis
Algebra and Number Theory

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10.1007/s00020-014-2184-3

Cite this

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title = "Boundary Interpolation for Slice Hyperholomorphic Schur Functions",

abstract = "A boundary Nevanlinna–Pick interpolation problem is posed and solved in the quaternionic setting. Given nonnegative real numbers (Formula presenred.), quaternions p1,…,pN all of modulus 1, so that the 2-spheres determined by each point do not intersect and pu ≠ 1 for u = 1,…, N, and quaternions s1,…, sN, we wish to find a slice hyperholomorphic Schur function s so that(Formula presenred.).(Formula presenred.).Our arguments rely on the theory of slice hyperholomorphic functions and reproducing kernel Hilbert spaces.",

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T1 - Boundary Interpolation for Slice Hyperholomorphic Schur Functions

AU - Abu-Ghanem, Khaled

AU - Alpay, Daniel

AU - Colombo, Fabrizio

AU - Kimsey, David P.

AU - Sabadini, Irene

PY - 2015/6/1

Y1 - 2015/6/1

N2 - A boundary Nevanlinna–Pick interpolation problem is posed and solved in the quaternionic setting. Given nonnegative real numbers (Formula presenred.), quaternions p1,…,pN all of modulus 1, so that the 2-spheres determined by each point do not intersect and pu ≠ 1 for u = 1,…, N, and quaternions s1,…, sN, we wish to find a slice hyperholomorphic Schur function s so that(Formula presenred.).(Formula presenred.).Our arguments rely on the theory of slice hyperholomorphic functions and reproducing kernel Hilbert spaces.

AB - A boundary Nevanlinna–Pick interpolation problem is posed and solved in the quaternionic setting. Given nonnegative real numbers (Formula presenred.), quaternions p1,…,pN all of modulus 1, so that the 2-spheres determined by each point do not intersect and pu ≠ 1 for u = 1,…, N, and quaternions s1,…, sN, we wish to find a slice hyperholomorphic Schur function s so that(Formula presenred.).(Formula presenred.).Our arguments rely on the theory of slice hyperholomorphic functions and reproducing kernel Hilbert spaces.

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KW - 47B32

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JO - Integral Equations and Operator Theory

JF - Integral Equations and Operator Theory

IS - 2

ER -

Boundary Interpolation for Slice Hyperholomorphic Schur Functions

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Keywords

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