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Interpolation by the derivatives of operator lipschitz functions. / Александров, Алексей Борисович.

Operator Theory: Advances and Applications. Springer Nature, 2018. стр. 83-95 (Operator Theory: Advances and Applications; Том 261).

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Harvard

Александров, АБ 2018, Interpolation by the derivatives of operator lipschitz functions. в Operator Theory: Advances and Applications. Operator Theory: Advances and Applications, Том. 261, Springer Nature, стр. 83-95. https://doi.org/10.1007/978-3-319-59078-3_4

APA

Александров, А. Б. (2018). Interpolation by the derivatives of operator lipschitz functions. в Operator Theory: Advances and Applications (стр. 83-95). (Operator Theory: Advances and Applications; Том 261). Springer Nature. https://doi.org/10.1007/978-3-319-59078-3_4

Vancouver

Александров АБ. Interpolation by the derivatives of operator lipschitz functions. в Operator Theory: Advances and Applications. Springer Nature. 2018. стр. 83-95. (Operator Theory: Advances and Applications). https://doi.org/10.1007/978-3-319-59078-3_4

Author

Александров, Алексей Борисович. / Interpolation by the derivatives of operator lipschitz functions. Operator Theory: Advances and Applications. Springer Nature, 2018. стр. 83-95 (Operator Theory: Advances and Applications).

BibTeX

@inbook{2c153e917af54dae802482a97f1964a2,
title = "Interpolation by the derivatives of operator lipschitz functions",
abstract = "Let Λ be a discrete subset of the real line ℝ. We prove that for every bounded function φ on Λ there exists an operator Lipschitz function f on ℝ such that f{\textquoteright} (t) = φ(t) for all t∈Λ. The same is true for the set of operator Lipschitz functions f on ℝ such that f{\textquoteright} coincides with the non-tangential boundary values of a bounded holomorphic function on the upper half-plane. In other words, for every bounded function φ on Λ there exists a commutator Lipschitz function f on the closed upper half-plane such that f{\textquoteright} (t) = φ(t) for all t∈Λ. The same is also true for some non-discrete countable sets Λ. Furthermore, we consider the case where Λ is a subset of the closed upper half-plane, Λ⊄ ℝ. Similar questions for commutator Lipschitz functions on a closed subset F of ℂ are also considered.",
keywords = "Commutator lipschitz functions, Interpolation, Operator lipschitz functions",
author = "Александров, {Алексей Борисович}",
note = "Publisher Copyright: {\textcopyright} Springer International Publishing AG, part of Springer Nature 2018.",
year = "2018",
doi = "10.1007/978-3-319-59078-3_4",
language = "English",
series = "Operator Theory: Advances and Applications",
publisher = "Springer Nature",
pages = "83--95",
booktitle = "Operator Theory",
address = "Germany",

}

RIS

TY - CHAP

T1 - Interpolation by the derivatives of operator lipschitz functions

AU - Александров, Алексей Борисович

N1 - Publisher Copyright: © Springer International Publishing AG, part of Springer Nature 2018.

PY - 2018

Y1 - 2018

N2 - Let Λ be a discrete subset of the real line ℝ. We prove that for every bounded function φ on Λ there exists an operator Lipschitz function f on ℝ such that f’ (t) = φ(t) for all t∈Λ. The same is true for the set of operator Lipschitz functions f on ℝ such that f’ coincides with the non-tangential boundary values of a bounded holomorphic function on the upper half-plane. In other words, for every bounded function φ on Λ there exists a commutator Lipschitz function f on the closed upper half-plane such that f’ (t) = φ(t) for all t∈Λ. The same is also true for some non-discrete countable sets Λ. Furthermore, we consider the case where Λ is a subset of the closed upper half-plane, Λ⊄ ℝ. Similar questions for commutator Lipschitz functions on a closed subset F of ℂ are also considered.

AB - Let Λ be a discrete subset of the real line ℝ. We prove that for every bounded function φ on Λ there exists an operator Lipschitz function f on ℝ such that f’ (t) = φ(t) for all t∈Λ. The same is true for the set of operator Lipschitz functions f on ℝ such that f’ coincides with the non-tangential boundary values of a bounded holomorphic function on the upper half-plane. In other words, for every bounded function φ on Λ there exists a commutator Lipschitz function f on the closed upper half-plane such that f’ (t) = φ(t) for all t∈Λ. The same is also true for some non-discrete countable sets Λ. Furthermore, we consider the case where Λ is a subset of the closed upper half-plane, Λ⊄ ℝ. Similar questions for commutator Lipschitz functions on a closed subset F of ℂ are also considered.

KW - Commutator lipschitz functions

KW - Interpolation

KW - Operator lipschitz functions

UR - http://www.scopus.com/inward/record.url?scp=85044778867&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-59078-3_4

DO - 10.1007/978-3-319-59078-3_4

M3 - Chapter

AN - SCOPUS:85044778867

T3 - Operator Theory: Advances and Applications

SP - 83

EP - 95

BT - Operator Theory

PB - Springer Nature

ER -

ID: 87315028