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On the Continuity of \(\tau \)-Wigner Pseudodifferential Operators

  • Lorenza D’EliaEmail author
Chapter
Part of the Applied and Numerical Harmonic Analysis book series (ANHA)

Abstract

In this survey, we recollect the latest results about the continuity of \(\tau \)-pseudodifferential operators. We obtain boundedness results for these operators with symbols in Wiener amalgam spaces for \(\tau \in (0,1)\), exhibiting a function of real parameter \(\tau \) which is an upper bound for the operator norm. In general, for \(\tau =0\) and \(\tau =1\) the corresponding operators are unbounded. For the well-known continuity properties of \(\tau \)-pseudodifferential operators with symbols in modulation spaces, we find an upper bound for the operator norm which does not depend on \(\tau \).

Keywords

\(\tau \)-Wigner distribution \(\tau \)-pseudodifferential operators Wiener amalgam spaces Modulation spaces 

2010 Mathematics Subject Classification

47G30 35S05 42B35 81S30 

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Dipartimento di MatematicaUniversità di TorinoTorinoItaly

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