On Polynomial Extension Property in N-Disc

Maciaszek, Krzysztof

doi:10.1007/s11785-019-00912-3

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Cited by 4 publications

(2 citation statements)

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“…For a fixed domain Ω, several papers have studied what analytic subvarieties gave rise to np pairs [3,8,14,11,12]. If Ω is suitably nice, the conclusion of these papers was that V had to be a holomorphic retract of Ω for (Ω, V ) to be an np pair.…”

Section: Introductionmentioning

confidence: 99%

Complete Norm Preserving Extensions of Holomorphic Functions

Agler¹,

Kosiński²,

McCarthy³

2022

Preprint

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We show that for every connected analytic subvariety V there is a pseudoconvex set Ω such that every bounded matrix-valued holomorphic function on V extends isometrically to Ω. We prove that if V is two analytic disks intersecting at one point, if every bounded scalar valued holomorphic function extends isometrically to Ω, then so does every matrix-valued function. In the special case that Ω is the symmetrized bidisk, we show that this cannot be done by finding a linear isometric extension from the functions that vanish at one point.

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Section: Introductionmentioning

confidence: 99%

Complete Norm Preserving Extensions of Holomorphic Functions

Agler¹,

Kosiński²,

McCarthy³

2022

Preprint

View full text Add to dashboard Cite

show abstract

“…2017/26/E/ST1/00723. subsets V, see [9,10], and [11]. The problem in D 3 is completely solved only with the additional assumption that the extension operator may be chosen to be linear (cf.…”

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confidence: 99%