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Averaged Wave Operators and Complex-symmetric Operators. / Bessonov, Roman; Kapustin, Vladimir.

In: Complex Analysis and Operator Theory, Vol. 10, No. 6, 01.08.2016, p. 1213-1226.

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

Harvard

Bessonov, R & Kapustin, V 2016, 'Averaged Wave Operators and Complex-symmetric Operators', Complex Analysis and Operator Theory, vol. 10, no. 6, pp. 1213-1226. https://doi.org/10.1007/s11785-015-0496-1

APA

Bessonov, R., & Kapustin, V. (2016). Averaged Wave Operators and Complex-symmetric Operators. Complex Analysis and Operator Theory, 10(6), 1213-1226. https://doi.org/10.1007/s11785-015-0496-1

Vancouver

Bessonov R, Kapustin V. Averaged Wave Operators and Complex-symmetric Operators. Complex Analysis and Operator Theory. 2016 Aug 1;10(6):1213-1226. https://doi.org/10.1007/s11785-015-0496-1

Author

Bessonov, Roman ; Kapustin, Vladimir. / Averaged Wave Operators and Complex-symmetric Operators. In: Complex Analysis and Operator Theory. 2016 ; Vol. 10, No. 6. pp. 1213-1226.

BibTeX

@article{db72fe6ed7184f7eaac63bd63de05722,
title = "Averaged Wave Operators and Complex-symmetric Operators",
abstract = "We study the behaviour of sequences U2nXU1-n, where U1, U2 are unitary operators, whose spectral measures are singular with respect to the Lebesgue measure, and the commutator XU1- U2X is small in a sense. The conjecture about the weak averaged convergence of the difference U2nXU1-n-U2-nXU1n to the zero operator is discussed and its connection with complex-symmetric operators is established in a general situation. For a model case where U1= U2 is the unitary operator of multiplication by z on L2(μ) , sufficient conditions for the convergence as in the Conjecture are given in terms of kernels of integral operators.",
keywords = "Ces{\`a}ro means, Singular spectral measure, Wave operators",
author = "Roman Bessonov and Vladimir Kapustin",
year = "2016",
month = aug,
day = "1",
doi = "10.1007/s11785-015-0496-1",
language = "English",
volume = "10",
pages = "1213--1226",
journal = "Complex Analysis and Operator Theory",
issn = "1661-8254",
publisher = "Birkh{\"a}user Verlag AG",
number = "6",

}

RIS

TY - JOUR

T1 - Averaged Wave Operators and Complex-symmetric Operators

AU - Bessonov, Roman

AU - Kapustin, Vladimir

PY - 2016/8/1

Y1 - 2016/8/1

N2 - We study the behaviour of sequences U2nXU1-n, where U1, U2 are unitary operators, whose spectral measures are singular with respect to the Lebesgue measure, and the commutator XU1- U2X is small in a sense. The conjecture about the weak averaged convergence of the difference U2nXU1-n-U2-nXU1n to the zero operator is discussed and its connection with complex-symmetric operators is established in a general situation. For a model case where U1= U2 is the unitary operator of multiplication by z on L2(μ) , sufficient conditions for the convergence as in the Conjecture are given in terms of kernels of integral operators.

AB - We study the behaviour of sequences U2nXU1-n, where U1, U2 are unitary operators, whose spectral measures are singular with respect to the Lebesgue measure, and the commutator XU1- U2X is small in a sense. The conjecture about the weak averaged convergence of the difference U2nXU1-n-U2-nXU1n to the zero operator is discussed and its connection with complex-symmetric operators is established in a general situation. For a model case where U1= U2 is the unitary operator of multiplication by z on L2(μ) , sufficient conditions for the convergence as in the Conjecture are given in terms of kernels of integral operators.

KW - Cesàro means

KW - Singular spectral measure

KW - Wave operators

UR - http://www.scopus.com/inward/record.url?scp=84944706293&partnerID=8YFLogxK

U2 - 10.1007/s11785-015-0496-1

DO - 10.1007/s11785-015-0496-1

M3 - Article

AN - SCOPUS:84944706293

VL - 10

SP - 1213

EP - 1226

JO - Complex Analysis and Operator Theory

JF - Complex Analysis and Operator Theory

SN - 1661-8254

IS - 6

ER -

ID: 36320944