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.
Freie Schlagwörter
Matrix symbol
Szegö-type theorem
Trace formula
Klassifikation (DDC)
510
Normschlagwörter (GND)
Asymptotik
Asymptotische Entwicklung
Spurklassenoperator
Toeplitz-Grenzwertsatz
Toeplitz-Operator
Beitragende/r
Prof. Dr. Bernd Silbermann
Prof. Dr. Igor Simonenko
Den akademischen Grad verleihende / prüfende Institution