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Toeplitz Operators in the Herglotz Space

Grigori Rozenblioum (Institutionen för matematiska vetenskaper, matematik) ; N. Vasilevski
Integral Equations and Operator Theory (0378-620X). Vol. 86 (2016), 3, p. 409-438.
[Artikel, refereegranskad vetenskaplig]

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.

Nyckelord: Bergman type spaces, Helmholtz equation, Toeplitz operators, bergman spaces, Mathematics

Denna post skapades 2016-12-09. Senast ändrad 2017-02-01.
CPL Pubid: 245988


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Institutionen för matematiska vetenskaper, matematik (2005-2016)


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