A new way of proof of Szegö-type theorems is
presented. The idea of the proof is based on the
construction of "almost" inverse operator to
the finite section T_n(a) of a Toeplitz operator T(a),
which is close to the inverse operator in the trace
norm (these "almost" inverses are well-known).
This way of proof gives the possibility to write
another representation for the second constant
E_f(a), and in the scalar case to receive a
shorter representation. Another observation is
that the convergence in these theorems is
strongly dependent on the smoothness of the
generating function a.
| Identifer | oai:union.ndltd.org:DRESDEN/oai:qucosa:de:qucosa:18666 |
| Date | 15 October 2002 |
| Creators | Vasilyev, Vladimir |
| Contributors | Silbermann, Bernd, Simonenko, Igor, Technische Universität Chemnitz |
| Source Sets | Hochschulschriftenserver (HSSS) der SLUB Dresden |
| Language | English |
| Detected Language | English |
| Type | doc-type:masterThesis, info:eu-repo/semantics/masterThesis, doc-type:Text |
| Rights | info:eu-repo/semantics/openAccess |
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