Research output: Contribution to journal › Article
Subspaces of C^infty invariant under the differentiation. / Aleman, Alexandru; Baranov, Anton; Belov, Yurii.
In: Journal of Functional Analysis, Vol. 268, No. 8, 2015, p. 2421–2439.Research output: Contribution to journal › Article
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TY - JOUR
T1 - Subspaces of C^infty invariant under the differentiation
AU - Aleman, Alexandru
AU - Baranov, Anton
AU - Belov, Yurii
PY - 2015
Y1 - 2015
N2 - Let L be a proper differentiation invariant subspace of C∞(a,b) such that the restriction operator 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 , 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 - Let L be a proper differentiation invariant subspace of C∞(a,b) such that the restriction operator 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 , 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.
KW - Spectral synthesis
KW - Entire functions
KW - Paley–Wiener spaces
KW - Invariant subspaces
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: 5764716