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L–Invariant Fock–Carleson Type Measures for Derivatives of Order k and the Corresponding Toeplitz Operators

Journal article
Authors K. Esmeral
Grigori Rozenblioum
N. Vasilevski
Published in Journal of Mathematical Sciences
Volume 242
Issue 2
Pages 337-358
ISSN 1072-3374
Publication year 2019
Published at Department of Mathematical Sciences
Pages 337-358
Language en
Subject categories Geometry, Mathematical Analysis, Algebra and Logic


Our purpose is to characterize the so-called horizontal Fock–Carleson type measures for derivatives of order k (we write it k-hFC for short) for the Fock space as well as the Toeplitz operators generated by sesquilinear forms given by them. We introduce real coderivatives of k-hFC type measures and show that the C*-algebra generated by Toeplitz operators with the corresponding class of symbols is commutative and isometrically isomorphic to a certain C*-subalgebra of L∞(ℝn). The above results are extended to measures that are invariant under translations along Lagrangian planes. © 2019, Springer Science+Business Media, LLC, part of Springer Nature.

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