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Canonical systems with discrete spectrum. / Romanov, Roman; Woracek, Harald.

In: Journal of Functional Analysis, Vol. 278, No. 4, 108318, 01.03.2020.

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

Harvard

Romanov, R & Woracek, H 2020, 'Canonical systems with discrete spectrum', Journal of Functional Analysis, vol. 278, no. 4, 108318. https://doi.org/10.1016/j.jfa.2019.108318

APA

Romanov, R., & Woracek, H. (2020). Canonical systems with discrete spectrum. Journal of Functional Analysis, 278(4), [108318]. https://doi.org/10.1016/j.jfa.2019.108318

Vancouver

Romanov R, Woracek H. Canonical systems with discrete spectrum. Journal of Functional Analysis. 2020 Mar 1;278(4). 108318. https://doi.org/10.1016/j.jfa.2019.108318

Author

Romanov, Roman ; Woracek, Harald. / Canonical systems with discrete spectrum. In: Journal of Functional Analysis. 2020 ; Vol. 278, No. 4.

BibTeX

@article{f8f08f93fc004cbbb2da10a0157fa56c,
title = "Canonical systems with discrete spectrum",
abstract = "We study spectral properties of two-dimensional canonical systems y′(t)=zJH(t)y(t), t∈[a,b), where the Hamiltonian H is locally integrable on [a,b), positive semidefinite, and Weyl's limit point case takes place at b. We answer the following questions explicitly in terms of H: Is the spectrum of the associated selfadjoint operator discrete? If it is discrete, what is its asymptotic distribution? Here asymptotic distribution means summability and limit superior conditions relative to comparison functions growing sufficiently fast. Making an analogy with complex analysis, this corresponds to convergence class and type w.r.t. proximate orders having order larger than 1. It is a surprising fact that these properties depend only on the diagonal entries of H. In 1968 L.de Branges posed the following question as a fundamental problem: Which Hamiltonians are the structure Hamiltonian of some de Branges space? We give a complete and explicit answer.",
keywords = "Canonical system, de Branges space, Discrete spectrum, Operator ideal, OPERATORS",
author = "Roman Romanov and Harald Woracek",
year = "2020",
month = mar,
day = "1",
doi = "10.1016/j.jfa.2019.108318",
language = "English",
volume = "278",
journal = "Journal of Functional Analysis",
issn = "0022-1236",
publisher = "Elsevier",
number = "4",

}

RIS

TY - JOUR

T1 - Canonical systems with discrete spectrum

AU - Romanov, Roman

AU - Woracek, Harald

PY - 2020/3/1

Y1 - 2020/3/1

N2 - We study spectral properties of two-dimensional canonical systems y′(t)=zJH(t)y(t), t∈[a,b), where the Hamiltonian H is locally integrable on [a,b), positive semidefinite, and Weyl's limit point case takes place at b. We answer the following questions explicitly in terms of H: Is the spectrum of the associated selfadjoint operator discrete? If it is discrete, what is its asymptotic distribution? Here asymptotic distribution means summability and limit superior conditions relative to comparison functions growing sufficiently fast. Making an analogy with complex analysis, this corresponds to convergence class and type w.r.t. proximate orders having order larger than 1. It is a surprising fact that these properties depend only on the diagonal entries of H. In 1968 L.de Branges posed the following question as a fundamental problem: Which Hamiltonians are the structure Hamiltonian of some de Branges space? We give a complete and explicit answer.

AB - We study spectral properties of two-dimensional canonical systems y′(t)=zJH(t)y(t), t∈[a,b), where the Hamiltonian H is locally integrable on [a,b), positive semidefinite, and Weyl's limit point case takes place at b. We answer the following questions explicitly in terms of H: Is the spectrum of the associated selfadjoint operator discrete? If it is discrete, what is its asymptotic distribution? Here asymptotic distribution means summability and limit superior conditions relative to comparison functions growing sufficiently fast. Making an analogy with complex analysis, this corresponds to convergence class and type w.r.t. proximate orders having order larger than 1. It is a surprising fact that these properties depend only on the diagonal entries of H. In 1968 L.de Branges posed the following question as a fundamental problem: Which Hamiltonians are the structure Hamiltonian of some de Branges space? We give a complete and explicit answer.

KW - Canonical system

KW - de Branges space

KW - Discrete spectrum

KW - Operator ideal

KW - OPERATORS

UR - http://www.scopus.com/inward/record.url?scp=85075528855&partnerID=8YFLogxK

U2 - 10.1016/j.jfa.2019.108318

DO - 10.1016/j.jfa.2019.108318

M3 - Article

AN - SCOPUS:85075528855

VL - 278

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

SN - 0022-1236

IS - 4

M1 - 108318

ER -

ID: 50903088