Toeplitz operators with frequency modulated semi-almost periodic symbols |
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Authors: | A Böttcher S Grudsky I Spitkovsky |
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Institution: | 1. Fakult?t für Mathematik, TU Chemnitz, 09107, Chemnitz, Germany 2. Faculty of Mechanics and Mathematics, Rostov-on-Don State University, Bolshaya Sadovaya 105, 344711, Rostov-on-Don, Russian Federation 3. Department of Mathematics, The College of William and Mary, 23187-8795, Williamsburg, VA
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Abstract: | It is well known that amplitude modulation does not affect Fredholmness of Toeplitz operators. The same is true for frequency
modulation provided the symbol of the operator is piecewise continuous. In this article, it is shown that frequency modulation
can destroy Fredholmness for Toeplitz operators with almost periodic symbols; the corresponding example is based on the observation
that certain almost periodic functions become semi-almost periodic functions after appropriate frequency modulation. Moreover,
this article contains several results that can be employed in order to decide whether a Toeplitz operator with a frequency
modulated semi-almost periodic symbol is Fredholm. |
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Keywords: | primary 47B35 secondary 42A75 46J15 47A53 |
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