New York Journal of Mathematics
Volume 24 (2018), 419-428


Mishko Mitkovski

Basis properties of complex exponentials and invertibility of Toeplitz operators

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Published: July 25, 2018
Keywords: complex exponentials, Toeplitz operators, reproducing kernels, inner function.
Subject: 30D20

We give a criterion for basicity of a sequence of complex exponentials in terms of the invertibility properties of a certain naturally associated Toeplitz operator. The criterion is similar to the well-known criterion of Hruschev, Nikolskii and Pavlov, the main difference being that we don't require preliminary translation of the frequency sequence to the upper half-plane.


Research supported in part by National Science Foundation DMS grant No. 1600874.

Author information

Department of Mathematical Sciences, Clemson University, O-110 Martin Hall, Box 340975, Clemson, SC 29634, USA