Standard

Toeplitz Operators in the Herglotz Space. / Rozenblum, Grigori; Vasilevski, Nikolai.

In: Integral Equations and Operator Theory, Vol. 86, No. 3, 01.11.2016, p. 409-438.

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

Harvard

Rozenblum, G & Vasilevski, N 2016, 'Toeplitz Operators in the Herglotz Space', Integral Equations and Operator Theory, vol. 86, no. 3, pp. 409-438. https://doi.org/10.1007/s00020-016-2331-0

APA

Rozenblum, G., & Vasilevski, N. (2016). Toeplitz Operators in the Herglotz Space. Integral Equations and Operator Theory, 86(3), 409-438. https://doi.org/10.1007/s00020-016-2331-0

Vancouver

Rozenblum G, Vasilevski N. Toeplitz Operators in the Herglotz Space. Integral Equations and Operator Theory. 2016 Nov 1;86(3):409-438. https://doi.org/10.1007/s00020-016-2331-0

Author

Rozenblum, Grigori ; Vasilevski, Nikolai. / Toeplitz Operators in the Herglotz Space. In: Integral Equations and Operator Theory. 2016 ; Vol. 86, No. 3. pp. 409-438.

BibTeX

@article{49e2fee6dd744d9885a4660e51d859ab,
title = "Toeplitz Operators in the Herglotz Space",
abstract = "We define and study Toeplitz operators in the space of Herglotz solutions of the Helmholtz equation in Rd. Since the most traditional definition of Toeplitz operators via Bergman-type projection is not available here, we use the approach based upon the reproducing kernel nature of the Herglotz space and sesquilinear forms, which results in a meaningful theory. For two important patterns of sesquilinear forms we discuss a number of properties, including the uniqueness of determining the symbols from the operator, the finite rank property, the conditions for boundedness and compactness, spectral properties, certain algebraic relations.",
keywords = "Bergman type spaces, Helmholtz equation, Toeplitz operators",
author = "Grigori Rozenblum and Nikolai Vasilevski",
year = "2016",
month = nov,
day = "1",
doi = "10.1007/s00020-016-2331-0",
language = "English",
volume = "86",
pages = "409--438",
journal = "Integral Equations and Operator Theory",
issn = "0378-620X",
publisher = "Birkh{\"a}user Verlag AG",
number = "3",

}

RIS

TY - JOUR

T1 - Toeplitz Operators in the Herglotz Space

AU - Rozenblum, Grigori

AU - Vasilevski, Nikolai

PY - 2016/11/1

Y1 - 2016/11/1

N2 - We define and study Toeplitz operators in the space of Herglotz solutions of the Helmholtz equation in Rd. Since the most traditional definition of Toeplitz operators via Bergman-type projection is not available here, we use the approach based upon the reproducing kernel nature of the Herglotz space and sesquilinear forms, which results in a meaningful theory. For two important patterns of sesquilinear forms we discuss a number of properties, including the uniqueness of determining the symbols from the operator, the finite rank property, the conditions for boundedness and compactness, spectral properties, certain algebraic relations.

AB - We define and study Toeplitz operators in the space of Herglotz solutions of the Helmholtz equation in Rd. Since the most traditional definition of Toeplitz operators via Bergman-type projection is not available here, we use the approach based upon the reproducing kernel nature of the Herglotz space and sesquilinear forms, which results in a meaningful theory. For two important patterns of sesquilinear forms we discuss a number of properties, including the uniqueness of determining the symbols from the operator, the finite rank property, the conditions for boundedness and compactness, spectral properties, certain algebraic relations.

KW - Bergman type spaces

KW - Helmholtz equation

KW - Toeplitz operators

UR - http://www.scopus.com/inward/record.url?scp=84994389322&partnerID=8YFLogxK

U2 - 10.1007/s00020-016-2331-0

DO - 10.1007/s00020-016-2331-0

M3 - Article

AN - SCOPUS:84994389322

VL - 86

SP - 409

EP - 438

JO - Integral Equations and Operator Theory

JF - Integral Equations and Operator Theory

SN - 0378-620X

IS - 3

ER -

ID: 50650259