Toeplitz Operators in the Herglotz Space
Journal article, 2016

We define and study Toeplitz operators in the space of Herglotz solutions of the Helmholtz equation in . 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.

Helmholtz equation

Bergman type spaces


bergman spaces

Toeplitz operators


Grigori Rozenblioum

Chalmers, Mathematical Sciences, Mathematics

University of Gothenburg

N. Vasilevski

Centro de Investigacion y de Estudios Avanzados Centro de Investigacion y de Estudios Avanzados (CINVESTAV)

Integral Equations and Operator Theory

0378-620X (ISSN) 1420-8989 (eISSN)

Vol. 86 3 409-438

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