Isometric embeddings of the spaces KΘ in the upper half-plane

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Isometric embeddings of the spaces K_Θ in the upper half-plane. / Baranov, A.

In: Journal of Mathematical Sciences, Vol. 105, No. 5, 01.01.2001, p. 2319-2329.

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Baranov, A. / Isometric embeddings of the spaces K_Θ in the upper half-plane. In: Journal of Mathematical Sciences. 2001 ; Vol. 105, No. 5. pp. 2319-2329.

BibTeX

@article{01afd1199ece4a1d8fae37aafcf230cd,

title = "Isometric embeddings of the spaces KΘ in the upper half-plane",

abstract = "Let Θ be an interior function in the upper half-plane. Positive measures μ on the real line ℝ such that ∫ℝ|f| 2dμ = ∥f∥2 2 for all f ∈ K Θ = H2 ⊖ΘH2 (i.e., the embedding KΘ ⊂ L2(μ) is isometric) are studied. A similar problem for the unit disk was considered by A. B. Aleksandrov. In the case of the upper half-plane and special interior functions, such measures were described by De Branges. The goal of this paper is to explain why these results are essentially different. As is shown, the fact that the isomterty fails is connected with the existence of the finite angular derivative and can be expressed in terms of factorization parameters of Θ. Owing to this results, it is possible to formulate a criterion (in terms of zeros of the generating entire function E) for an orthogonal system of reproducing kernels to be a basis for the space H(E).",

author = "A. Baranov",

year = "2001",

month = jan,

day = "1",

doi = "10.1023/A:1011309128229",

language = "English",

volume = "105",

pages = "2319--2329",

journal = "Journal of Mathematical Sciences",

issn = "1072-3374",

publisher = "Springer Nature",

number = "5",

}

RIS

TY - JOUR

T1 - Isometric embeddings of the spaces KΘ in the upper half-plane

AU - Baranov, A.

PY - 2001/1/1

Y1 - 2001/1/1

N2 - Let Θ be an interior function in the upper half-plane. Positive measures μ on the real line ℝ such that ∫ℝ|f| 2dμ = ∥f∥2 2 for all f ∈ K Θ = H2 ⊖ΘH2 (i.e., the embedding KΘ ⊂ L2(μ) is isometric) are studied. A similar problem for the unit disk was considered by A. B. Aleksandrov. In the case of the upper half-plane and special interior functions, such measures were described by De Branges. The goal of this paper is to explain why these results are essentially different. As is shown, the fact that the isomterty fails is connected with the existence of the finite angular derivative and can be expressed in terms of factorization parameters of Θ. Owing to this results, it is possible to formulate a criterion (in terms of zeros of the generating entire function E) for an orthogonal system of reproducing kernels to be a basis for the space H(E).

AB - Let Θ be an interior function in the upper half-plane. Positive measures μ on the real line ℝ such that ∫ℝ|f| 2dμ = ∥f∥2 2 for all f ∈ K Θ = H2 ⊖ΘH2 (i.e., the embedding KΘ ⊂ L2(μ) is isometric) are studied. A similar problem for the unit disk was considered by A. B. Aleksandrov. In the case of the upper half-plane and special interior functions, such measures were described by De Branges. The goal of this paper is to explain why these results are essentially different. As is shown, the fact that the isomterty fails is connected with the existence of the finite angular derivative and can be expressed in terms of factorization parameters of Θ. Owing to this results, it is possible to formulate a criterion (in terms of zeros of the generating entire function E) for an orthogonal system of reproducing kernels to be a basis for the space H(E).

UR - http://www.scopus.com/inward/record.url?scp=7444257251&partnerID=8YFLogxK

U2 - 10.1023/A:1011309128229

DO - 10.1023/A:1011309128229

M3 - Article

AN - SCOPUS:7444257251

VL - 105

SP - 2319

EP - 2329

JO - Journal of Mathematical Sciences

JF - Journal of Mathematical Sciences

SN - 1072-3374

IS - 5

ER -

ID: 32721389