Cauchy–de Branges Spaces, Geometry of Their Reproducing Kernels and Multiplication Operators

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Cauchy–de Branges Spaces, Geometry of Their Reproducing Kernels and Multiplication Operators. / Баранов, Антон Дмитриевич.

In: Milan Journal of Mathematics, Vol. 91, No. 1, 01.06.2023, p. 97-130.

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

BibTeX

@article{b8de5ef99e8b4a34a36dd912b82610c9,

title = "Cauchy–de Branges Spaces, Geometry of Their Reproducing Kernels and Multiplication Operators",

abstract = "Cauchy–de Branges spaces are Hilbert spaces of entire functions defined in terms of Cauchy transforms of discrete measures on the plane and generalizing the classical de Branges theory. We consider extensions of two important properties of de Branges spaces to this, more general, setting. First, we discuss geometric properties (completeness, Riesz bases) of systems of reproducing kernels corresponding to the zeros of certain entire functions associated to the space. In the case of de Branges spaces they correspond to orthogonal bases of reproducing kernels. The second theme of the paper is a characterization of the density of the domain of multiplication by z in Cauchy–de Branges spaces.",

keywords = "преобразование Коши, целая функция, воспроизводящее ядро, Cauchy transform, Reproducing kernel, de Branges space",

author = "Баранов, {Антон Дмитриевич}",

year = "2023",

month = jun,

day = "1",

doi = "10.1007/s00032-023-00378-1",

language = "English",

volume = "91",

pages = "97--130",

journal = "Milan Journal of Mathematics",

issn = "1424-9286",

publisher = "Birkh{\"a}user Verlag AG",

number = "1",

}

RIS

TY - JOUR

T1 - Cauchy–de Branges Spaces, Geometry of Their Reproducing Kernels and Multiplication Operators

AU - Баранов, Антон Дмитриевич

PY - 2023/6/1

Y1 - 2023/6/1

N2 - Cauchy–de Branges spaces are Hilbert spaces of entire functions defined in terms of Cauchy transforms of discrete measures on the plane and generalizing the classical de Branges theory. We consider extensions of two important properties of de Branges spaces to this, more general, setting. First, we discuss geometric properties (completeness, Riesz bases) of systems of reproducing kernels corresponding to the zeros of certain entire functions associated to the space. In the case of de Branges spaces they correspond to orthogonal bases of reproducing kernels. The second theme of the paper is a characterization of the density of the domain of multiplication by z in Cauchy–de Branges spaces.

AB - Cauchy–de Branges spaces are Hilbert spaces of entire functions defined in terms of Cauchy transforms of discrete measures on the plane and generalizing the classical de Branges theory. We consider extensions of two important properties of de Branges spaces to this, more general, setting. First, we discuss geometric properties (completeness, Riesz bases) of systems of reproducing kernels corresponding to the zeros of certain entire functions associated to the space. In the case of de Branges spaces they correspond to orthogonal bases of reproducing kernels. The second theme of the paper is a characterization of the density of the domain of multiplication by z in Cauchy–de Branges spaces.

KW - преобразование Коши, целая функция, воспроизводящее ядро

KW - Cauchy transform

KW - Reproducing kernel

KW - de Branges space

UR - https://link.springer.com/article/10.1007/s00032-023-00378-1

UR - https://www.mendeley.com/catalogue/47efcb95-09d1-3f5c-b21a-d1e44915dff8/

U2 - 10.1007/s00032-023-00378-1

DO - 10.1007/s00032-023-00378-1

M3 - Article

VL - 91

SP - 97

EP - 130

JO - Milan Journal of Mathematics

JF - Milan Journal of Mathematics

SN - 1424-9286

IS - 1

ER -

ID: 115315258