Trace approximations of products of truncated Toeplitz operators (Q2882762)
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scientific article; zbMATH DE number 6031473
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Trace approximations of products of truncated Toeplitz operators |
scientific article; zbMATH DE number 6031473 |
Statements
7 May 2012
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trace approximation
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truncated Toeplitz operator
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continuous-time stationary process
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long-memory
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spectral density
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singularity
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fractional Riesz-Bessel motion
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Trace approximations of products of truncated Toeplitz operators (English)
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The paper is devoted to the problem of approximation of the traces of products of truncated Toeplitz operators generated by integrable real symmetric functions defined on the real line, and estimation of the corresponding errors. The results have a great importance for various branches of mathematics, especially in the statistical analysis of continuous-time stationary processes. The paper has four sections. After an introduction, in the second section the main results are presented. An explicit second-order asymptotic expansion for the trace of a product of two truncated Toeplitz operators is obtained. In the third section some auxiliary results are given, and in the last section of the paper the detailed proofs are made.
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