Commutator Lipschitz Functions and Analytic Continuation

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Commutator Lipschitz Functions and Analytic Continuation. / Александров, Алексей Борисович.

In: Journal of Mathematical Sciences (United States), Vol. 215, No. 5, 01.06.2016, p. 543-551.

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

BibTeX

@article{33aad9452d774ff4aea36bd150be4bde,

title = "Commutator Lipschitz Functions and Analytic Continuation",

abstract = "Let F0 and F be perfect subsets of the complex plane ℂ. Assume that F0 ⊂ F and the set Ω = d e f F\ F0 is open. We say that a continuous function f : F → ℂ is an analytic continuation of a function f0 : F0 → ℂ if f is analytic on Ω and f|F0 = f0. In the paper, it is proved that if F is bounded, then the commutator Lipschitz seminorm of the analytic continuation f coincides with the commutator Lipschitz seminorm of f0. The same is true for unbounded F if some natural restrictions concerning the behavior of f at infinity are imposed.",

author = "Александров, {Алексей Борисович}",

note = "Publisher Copyright: {\textcopyright} 2016, Springer Science+Business Media New York.",

year = "2016",

month = jun,

day = "1",

doi = "10.1007/s10958-016-2859-1",

language = "English",

volume = "215",

pages = "543--551",

journal = "Journal of Mathematical Sciences",

issn = "1072-3374",

publisher = "Springer Nature",

number = "5",

}

RIS

TY - JOUR

T1 - Commutator Lipschitz Functions and Analytic Continuation

AU - Александров, Алексей Борисович

PY - 2016/6/1

Y1 - 2016/6/1

N2 - Let F0 and F be perfect subsets of the complex plane ℂ. Assume that F0 ⊂ F and the set Ω = d e f F\ F0 is open. We say that a continuous function f : F → ℂ is an analytic continuation of a function f0 : F0 → ℂ if f is analytic on Ω and f|F0 = f0. In the paper, it is proved that if F is bounded, then the commutator Lipschitz seminorm of the analytic continuation f coincides with the commutator Lipschitz seminorm of f0. The same is true for unbounded F if some natural restrictions concerning the behavior of f at infinity are imposed.

AB - Let F0 and F be perfect subsets of the complex plane ℂ. Assume that F0 ⊂ F and the set Ω = d e f F\ F0 is open. We say that a continuous function f : F → ℂ is an analytic continuation of a function f0 : F0 → ℂ if f is analytic on Ω and f|F0 = f0. In the paper, it is proved that if F is bounded, then the commutator Lipschitz seminorm of the analytic continuation f coincides with the commutator Lipschitz seminorm of f0. The same is true for unbounded F if some natural restrictions concerning the behavior of f at infinity are imposed.

UR - http://www.scopus.com/inward/record.url?scp=84965066396&partnerID=8YFLogxK

U2 - 10.1007/s10958-016-2859-1

DO - 10.1007/s10958-016-2859-1

M3 - Article

AN - SCOPUS:84965066396

VL - 215

SP - 543

EP - 551

JO - Journal of Mathematical Sciences

JF - Journal of Mathematical Sciences

SN - 1072-3374

IS - 5

ER -

ID: 87315430