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Subspaces of C∞ invariant under the differentiation. / Aleman, A.; Baranov, A.; Belov, Y.

In: Journal of Functional Analysis, Vol. 268, No. 8, 2015, p. 2421-2439.

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Harvard

Aleman, A, Baranov, A & Belov, Y 2015, 'Subspaces of C∞ invariant under the differentiation', Journal of Functional Analysis, vol. 268, no. 8, pp. 2421-2439. https://doi.org/10.1016/j.jfa.2015.01.002

APA

Aleman, A., Baranov, A., & Belov, Y. (2015). Subspaces of C∞ invariant under the differentiation. Journal of Functional Analysis, 268(8), 2421-2439. https://doi.org/10.1016/j.jfa.2015.01.002

Vancouver

Aleman A, Baranov A, Belov Y. Subspaces of C∞ invariant under the differentiation. Journal of Functional Analysis. 2015;268(8):2421-2439. https://doi.org/10.1016/j.jfa.2015.01.002

Author

Aleman, A. ; Baranov, A. ; Belov, Y. / Subspaces of C∞ invariant under the differentiation. In: Journal of Functional Analysis. 2015 ; Vol. 268, No. 8. pp. 2421-2439.

BibTeX

@article{f5e47506574d454c8cf2b371c488db0f,
title = "Subspaces of C∞ invariant under the differentiation",
abstract = "{\textcopyright} 2015 Elsevier Inc.Let L be a proper differentiation invariant subspace of C∞(a, b) such that the restriction operator ddx|L has a discrete spectrum Λ (counting with multiplicities). We prove that L is spanned by functions vanishing outside some closed interval I⊂(a, b) and monomial exponentials xkeλx corresponding to Λ if its density is strictly less than the critical value |I|2π, and moreover, we show that the result is not necessarily true when the density of Λ equals the critical value. This answers a question posed by the first author and B. Korenblum. Finally, if the residual part of L is trivial, then L is spanned by the monomial exponentials it contains.",
author = "A. Aleman and A. Baranov and Y. Belov",
year = "2015",
doi = "10.1016/j.jfa.2015.01.002",
language = "English",
volume = "268",
pages = "2421--2439",
journal = "Journal of Functional Analysis",
issn = "0022-1236",
publisher = "Elsevier",
number = "8",

}

RIS

TY - JOUR

T1 - Subspaces of C∞ invariant under the differentiation

AU - Aleman, A.

AU - Baranov, A.

AU - Belov, Y.

PY - 2015

Y1 - 2015

N2 - © 2015 Elsevier Inc.Let L be a proper differentiation invariant subspace of C∞(a, b) such that the restriction operator ddx|L has a discrete spectrum Λ (counting with multiplicities). We prove that L is spanned by functions vanishing outside some closed interval I⊂(a, b) and monomial exponentials xkeλx corresponding to Λ if its density is strictly less than the critical value |I|2π, and moreover, we show that the result is not necessarily true when the density of Λ equals the critical value. This answers a question posed by the first author and B. Korenblum. Finally, if the residual part of L is trivial, then L is spanned by the monomial exponentials it contains.

AB - © 2015 Elsevier Inc.Let L be a proper differentiation invariant subspace of C∞(a, b) such that the restriction operator ddx|L has a discrete spectrum Λ (counting with multiplicities). We prove that L is spanned by functions vanishing outside some closed interval I⊂(a, b) and monomial exponentials xkeλx corresponding to Λ if its density is strictly less than the critical value |I|2π, and moreover, we show that the result is not necessarily true when the density of Λ equals the critical value. This answers a question posed by the first author and B. Korenblum. Finally, if the residual part of L is trivial, then L is spanned by the monomial exponentials it contains.

U2 - 10.1016/j.jfa.2015.01.002

DO - 10.1016/j.jfa.2015.01.002

M3 - Article

VL - 268

SP - 2421

EP - 2439

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

SN - 0022-1236

IS - 8

ER -

ID: 3988655