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Differentiation in the Branges spaces and embedding theorems. / Baranov, A. D.

In: Journal of Mathematical Sciences, Vol. 101, No. 2, 01.01.2000, p. 2881-2913.

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

Harvard

Baranov, AD 2000, 'Differentiation in the Branges spaces and embedding theorems', Journal of Mathematical Sciences, vol. 101, no. 2, pp. 2881-2913. https://doi.org/10.1007/BF02672176

APA

Baranov, A. D. (2000). Differentiation in the Branges spaces and embedding theorems. Journal of Mathematical Sciences, 101(2), 2881-2913. https://doi.org/10.1007/BF02672176

Vancouver

Baranov AD. Differentiation in the Branges spaces and embedding theorems. Journal of Mathematical Sciences. 2000 Jan 1;101(2):2881-2913. https://doi.org/10.1007/BF02672176

Author

Baranov, A. D. / Differentiation in the Branges spaces and embedding theorems. In: Journal of Mathematical Sciences. 2000 ; Vol. 101, No. 2. pp. 2881-2913.

BibTeX

@article{b8e75b48e12f41b8b0dce4da1ee81533,
title = "Differentiation in the Branges spaces and embedding theorems",
abstract = "The boundedness conditions for the differentiation operator in Hilbert spaces of entire functions (Branges spaces) and conditions under which the embedding K⊖ ∪ L2(μ) holds in spaces K⊖ associated with the Branges spaces ℋ(E) are studied. Measures μ such that the above embedding is isometric are of special interest. It turns out that the condition E′/E ∈ H∞(C+) is sufficient for the boundedness of the differentiation operator in ℋ(E). Under certain restrictions on E, this condition is also necessary. However, this fact fails in the general case, which is demonstrated by the counterexamples constructed in this paper. The convex structure of the set of measures μ such that the embedding KĖ/E ∪ L2(μ) is isometric (the set of such measures was described by de Branges) is considered. Some classes of measures that are extreme points in the set of Branges measures are distinguished. Examples of measures that are not extreme points are also given. Bibliography: 7 titles.",
author = "Baranov, {A. D.}",
year = "2000",
month = jan,
day = "1",
doi = "10.1007/BF02672176",
language = "English",
volume = "101",
pages = "2881--2913",
journal = "Journal of Mathematical Sciences",
issn = "1072-3374",
publisher = "Springer Nature",
number = "2",

}

RIS

TY - JOUR

T1 - Differentiation in the Branges spaces and embedding theorems

AU - Baranov, A. D.

PY - 2000/1/1

Y1 - 2000/1/1

N2 - The boundedness conditions for the differentiation operator in Hilbert spaces of entire functions (Branges spaces) and conditions under which the embedding K⊖ ∪ L2(μ) holds in spaces K⊖ associated with the Branges spaces ℋ(E) are studied. Measures μ such that the above embedding is isometric are of special interest. It turns out that the condition E′/E ∈ H∞(C+) is sufficient for the boundedness of the differentiation operator in ℋ(E). Under certain restrictions on E, this condition is also necessary. However, this fact fails in the general case, which is demonstrated by the counterexamples constructed in this paper. The convex structure of the set of measures μ such that the embedding KĖ/E ∪ L2(μ) is isometric (the set of such measures was described by de Branges) is considered. Some classes of measures that are extreme points in the set of Branges measures are distinguished. Examples of measures that are not extreme points are also given. Bibliography: 7 titles.

AB - The boundedness conditions for the differentiation operator in Hilbert spaces of entire functions (Branges spaces) and conditions under which the embedding K⊖ ∪ L2(μ) holds in spaces K⊖ associated with the Branges spaces ℋ(E) are studied. Measures μ such that the above embedding is isometric are of special interest. It turns out that the condition E′/E ∈ H∞(C+) is sufficient for the boundedness of the differentiation operator in ℋ(E). Under certain restrictions on E, this condition is also necessary. However, this fact fails in the general case, which is demonstrated by the counterexamples constructed in this paper. The convex structure of the set of measures μ such that the embedding KĖ/E ∪ L2(μ) is isometric (the set of such measures was described by de Branges) is considered. Some classes of measures that are extreme points in the set of Branges measures are distinguished. Examples of measures that are not extreme points are also given. Bibliography: 7 titles.

UR - http://www.scopus.com/inward/record.url?scp=0010465573&partnerID=8YFLogxK

U2 - 10.1007/BF02672176

DO - 10.1007/BF02672176

M3 - Article

AN - SCOPUS:0010465573

VL - 101

SP - 2881

EP - 2913

JO - Journal of Mathematical Sciences

JF - Journal of Mathematical Sciences

SN - 1072-3374

IS - 2

ER -

ID: 32721314