Toeplitz Operators in the Herglotz Space
Artikel i vetenskaplig tidskrift, 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

Mathematics

bergman spaces

Toeplitz operators

Författare

Grigori Rozenblioum

Chalmers, Matematiska vetenskaper, Matematik

Göteborgs universitet

N. Vasilevski

Centro de Investigacion y de Estudios Avanzados (CINVESTAV)

Integral Equations and Operator Theory

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

Vol. 86 409-438

Drivkrafter

Hållbar utveckling

Ämneskategorier

Fysik

Annan fysik

DOI

10.1007/s00020-016-2331-0