Standard

Toeplitz operators via sesquilinear forms. / Rozenblum, Grigori; Vasilevski, Nikolai.

Operator Theory: Advances and Applications. Springer Nature, 2018. p. 287-304 (Operator Theory: Advances and Applications; Vol. 262).

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

Harvard

Rozenblum, G & Vasilevski, N 2018, Toeplitz operators via sesquilinear forms. in Operator Theory: Advances and Applications. Operator Theory: Advances and Applications, vol. 262, Springer Nature, pp. 287-304. https://doi.org/10.1007/978-3-319-62527-0_9

APA

Rozenblum, G., & Vasilevski, N. (2018). Toeplitz operators via sesquilinear forms. In Operator Theory: Advances and Applications (pp. 287-304). (Operator Theory: Advances and Applications; Vol. 262). Springer Nature. https://doi.org/10.1007/978-3-319-62527-0_9

Vancouver

Rozenblum G, Vasilevski N. Toeplitz operators via sesquilinear forms. In Operator Theory: Advances and Applications. Springer Nature. 2018. p. 287-304. (Operator Theory: Advances and Applications). https://doi.org/10.1007/978-3-319-62527-0_9

Author

Rozenblum, Grigori ; Vasilevski, Nikolai. / Toeplitz operators via sesquilinear forms. Operator Theory: Advances and Applications. Springer Nature, 2018. pp. 287-304 (Operator Theory: Advances and Applications).

BibTeX

@inbook{69197dfe296f44789fd207c14a2e1590,
title = "Toeplitz operators via sesquilinear forms",
abstract = "The classical theory of Toeplitz operators in spaces of analytic functions deals usually with symbols that are bounded measurable functions on the domain in question. A further extension of the theory was made for symbols being unbounded functions, measures, and compactly supported distributions, all of them subject to some restrictions. In the context of a reproducing kernel Hilbert space we propose a certain common framework, based upon the extensive use of the language of sesquilinear form, for definition of Toeplitz operators for a {\textquoteleft}maximally wide{\textquoteright} class of {\textquoteleft}highly singular{\textquoteright} symbols. Besides covering all previously considered cases, such an approach permits us to introduce a further substantial extension of the class of admissible symbols that generate bounded Toeplitz operators. Although our approach is unified for all reproducing kernel Hilbert spaces, concrete operator consideration are given for Toeplitz operators acting on the standard Fock space, on the standard Bergman space on the unit disk (two leading examples in the classical theory of Toeplitz operators), and on the so-called Herglotz space consisting of the solutions of the Helmholtz equation.",
keywords = "Bergman space, Fock space, Herglotz space, Reproducing kernel hilbert space, Sesquilinear form, Toeplitz operators",
author = "Grigori Rozenblum and Nikolai Vasilevski",
year = "2018",
month = jan,
day = "1",
doi = "10.1007/978-3-319-62527-0_9",
language = "English",
series = "Operator Theory: Advances and Applications",
publisher = "Springer Nature",
pages = "287--304",
booktitle = "Operator Theory",
address = "Germany",

}

RIS

TY - CHAP

T1 - Toeplitz operators via sesquilinear forms

AU - Rozenblum, Grigori

AU - Vasilevski, Nikolai

PY - 2018/1/1

Y1 - 2018/1/1

N2 - The classical theory of Toeplitz operators in spaces of analytic functions deals usually with symbols that are bounded measurable functions on the domain in question. A further extension of the theory was made for symbols being unbounded functions, measures, and compactly supported distributions, all of them subject to some restrictions. In the context of a reproducing kernel Hilbert space we propose a certain common framework, based upon the extensive use of the language of sesquilinear form, for definition of Toeplitz operators for a ‘maximally wide’ class of ‘highly singular’ symbols. Besides covering all previously considered cases, such an approach permits us to introduce a further substantial extension of the class of admissible symbols that generate bounded Toeplitz operators. Although our approach is unified for all reproducing kernel Hilbert spaces, concrete operator consideration are given for Toeplitz operators acting on the standard Fock space, on the standard Bergman space on the unit disk (two leading examples in the classical theory of Toeplitz operators), and on the so-called Herglotz space consisting of the solutions of the Helmholtz equation.

AB - The classical theory of Toeplitz operators in spaces of analytic functions deals usually with symbols that are bounded measurable functions on the domain in question. A further extension of the theory was made for symbols being unbounded functions, measures, and compactly supported distributions, all of them subject to some restrictions. In the context of a reproducing kernel Hilbert space we propose a certain common framework, based upon the extensive use of the language of sesquilinear form, for definition of Toeplitz operators for a ‘maximally wide’ class of ‘highly singular’ symbols. Besides covering all previously considered cases, such an approach permits us to introduce a further substantial extension of the class of admissible symbols that generate bounded Toeplitz operators. Although our approach is unified for all reproducing kernel Hilbert spaces, concrete operator consideration are given for Toeplitz operators acting on the standard Fock space, on the standard Bergman space on the unit disk (two leading examples in the classical theory of Toeplitz operators), and on the so-called Herglotz space consisting of the solutions of the Helmholtz equation.

KW - Bergman space

KW - Fock space

KW - Herglotz space

KW - Reproducing kernel hilbert space

KW - Sesquilinear form

KW - Toeplitz operators

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U2 - 10.1007/978-3-319-62527-0_9

DO - 10.1007/978-3-319-62527-0_9

M3 - Chapter

AN - SCOPUS:85044968013

T3 - Operator Theory: Advances and Applications

SP - 287

EP - 304

BT - Operator Theory

PB - Springer Nature

ER -

ID: 50650045