Interpolation by periods in a planar domain

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Interpolation by periods in a planar domain. / Dubashinskiy, M. B.

In: St. Petersburg Mathematical Journal, Vol. 28, No. 5, 01.01.2017, p. 597-669.

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

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Dubashinskiy, M. B. / Interpolation by periods in a planar domain. In: St. Petersburg Mathematical Journal. 2017 ; Vol. 28, No. 5. pp. 597-669.

BibTeX

@article{82029a6cc5cf4e4182560f5a23d64031,

title = "Interpolation by periods in a planar domain",

abstract = "Let Ω ⊂ ℝ2 be a countably connected domain. With any closed differential form of degree 1 in Ω with components in L2(Ω) one associates the sequence of its periods around the holes in Ω that is around the bounded connected components of ℝ2 \ Ω. For which Ω the collection of such period sequences coincides with ℓ2 We give an answer in terms of metric properties of holes in Ω.",

keywords = "Harmonic functions, Infinitely-connected domain, Interpolation, Periods of forms, Riesz basis",

author = "Dubashinskiy, {M. B.}",

year = "2017",

month = jan,

day = "1",

doi = "10.1090/spmj/1465",

language = "English",

volume = "28",

pages = "597--669",

journal = "St. Petersburg Mathematical Journal",

issn = "1061-0022",

publisher = "American Mathematical Society",

number = "5",

}

RIS

TY - JOUR

T1 - Interpolation by periods in a planar domain

AU - Dubashinskiy, M. B.

PY - 2017/1/1

Y1 - 2017/1/1

N2 - Let Ω ⊂ ℝ2 be a countably connected domain. With any closed differential form of degree 1 in Ω with components in L2(Ω) one associates the sequence of its periods around the holes in Ω that is around the bounded connected components of ℝ2 \ Ω. For which Ω the collection of such period sequences coincides with ℓ2 We give an answer in terms of metric properties of holes in Ω.

AB - Let Ω ⊂ ℝ2 be a countably connected domain. With any closed differential form of degree 1 in Ω with components in L2(Ω) one associates the sequence of its periods around the holes in Ω that is around the bounded connected components of ℝ2 \ Ω. For which Ω the collection of such period sequences coincides with ℓ2 We give an answer in terms of metric properties of holes in Ω.

KW - Harmonic functions

KW - Infinitely-connected domain

KW - Interpolation

KW - Periods of forms

KW - Riesz basis

UR - http://www.scopus.com/inward/record.url?scp=85026303105&partnerID=8YFLogxK

U2 - 10.1090/spmj/1465

DO - 10.1090/spmj/1465

M3 - Article

AN - SCOPUS:85026303105

VL - 28

SP - 597

EP - 669

JO - St. Petersburg Mathematical Journal

JF - St. Petersburg Mathematical Journal

SN - 1061-0022

IS - 5

ER -

ID: 36498082