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Clark measures and de Branges–Rovnyak spaces in several variables. / Aleksandrov, Aleksei B.; Doubtsov, Evgueni.

в: Complex Variables and Elliptic Equations, 03.11.2021.

Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование

Harvard

Aleksandrov, AB & Doubtsov, E 2021, 'Clark measures and de Branges–Rovnyak spaces in several variables', Complex Variables and Elliptic Equations. https://doi.org/10.1080/17476933.2021.1985480

APA

Aleksandrov, A. B., & Doubtsov, E. (2021). Clark measures and de Branges–Rovnyak spaces in several variables. Complex Variables and Elliptic Equations. https://doi.org/10.1080/17476933.2021.1985480

Vancouver

Aleksandrov AB, Doubtsov E. Clark measures and de Branges–Rovnyak spaces in several variables. Complex Variables and Elliptic Equations. 2021 Нояб. 3. https://doi.org/10.1080/17476933.2021.1985480

Author

Aleksandrov, Aleksei B. ; Doubtsov, Evgueni. / Clark measures and de Branges–Rovnyak spaces in several variables. в: Complex Variables and Elliptic Equations. 2021.

BibTeX

@article{4e2f07a49cd54756a06568d3eb91b0f1,
title = "Clark measures and de Branges–Rovnyak spaces in several variables",
abstract = "Let B-n denote the unit ball of C-n, n >= 1, and let D denote a finite product of B-nj, j >= 1. Given a non-constant holomorphic function b: D -> B-1, we study the corresponding family sigma(alpha) [6], alpha is an element of partial derivative B-1, of Clark measures on the distinguished boundary partial derivative D. We construct a natural unitary operator from the de Branges-Rovnyak space H(b) onto the Hardy space H-2 (sigma(alpha)). As an application, for D = B-n and an inner function I: B-n -> B-1, we show that the property sigma(1)[f] << sigma(1)[b] is directly related to the membership of an appropriate explicit function in H(b).",
keywords = "30J05, 31C10, 32A26, 32A35, 46E22, Cauchy integrals, Clark measures, de Branges–Rovnyak spaces, Hardy spaces, Henkin measures, inner functions, de Branges-Rovnyak spaces",
author = "Aleksandrov, {Aleksei B.} and Evgueni Doubtsov",
note = "Publisher Copyright: {\textcopyright} 2021 Informa UK Limited, trading as Taylor & Francis Group.",
year = "2021",
month = nov,
day = "3",
doi = "10.1080/17476933.2021.1985480",
language = "English",
journal = "Complex Variables and Elliptic Equations",
issn = "1747-6933",
publisher = "Taylor & Francis",

}

RIS

TY - JOUR

T1 - Clark measures and de Branges–Rovnyak spaces in several variables

AU - Aleksandrov, Aleksei B.

AU - Doubtsov, Evgueni

N1 - Publisher Copyright: © 2021 Informa UK Limited, trading as Taylor & Francis Group.

PY - 2021/11/3

Y1 - 2021/11/3

N2 - Let B-n denote the unit ball of C-n, n >= 1, and let D denote a finite product of B-nj, j >= 1. Given a non-constant holomorphic function b: D -> B-1, we study the corresponding family sigma(alpha) [6], alpha is an element of partial derivative B-1, of Clark measures on the distinguished boundary partial derivative D. We construct a natural unitary operator from the de Branges-Rovnyak space H(b) onto the Hardy space H-2 (sigma(alpha)). As an application, for D = B-n and an inner function I: B-n -> B-1, we show that the property sigma(1)[f] << sigma(1)[b] is directly related to the membership of an appropriate explicit function in H(b).

AB - Let B-n denote the unit ball of C-n, n >= 1, and let D denote a finite product of B-nj, j >= 1. Given a non-constant holomorphic function b: D -> B-1, we study the corresponding family sigma(alpha) [6], alpha is an element of partial derivative B-1, of Clark measures on the distinguished boundary partial derivative D. We construct a natural unitary operator from the de Branges-Rovnyak space H(b) onto the Hardy space H-2 (sigma(alpha)). As an application, for D = B-n and an inner function I: B-n -> B-1, we show that the property sigma(1)[f] << sigma(1)[b] is directly related to the membership of an appropriate explicit function in H(b).

KW - 30J05

KW - 31C10

KW - 32A26

KW - 32A35

KW - 46E22

KW - Cauchy integrals

KW - Clark measures

KW - de Branges–Rovnyak spaces

KW - Hardy spaces

KW - Henkin measures

KW - inner functions

KW - de Branges-Rovnyak spaces

UR - http://www.scopus.com/inward/record.url?scp=85118574852&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/334bd77c-b002-3915-87ff-b53564e8e5e7/

U2 - 10.1080/17476933.2021.1985480

DO - 10.1080/17476933.2021.1985480

M3 - Article

AN - SCOPUS:85118574852

JO - Complex Variables and Elliptic Equations

JF - Complex Variables and Elliptic Equations

SN - 1747-6933

ER -

ID: 88196958