Karlheinz Groechenig
Time-Frequency Partitions and Characterizations of Modulation Spaces with Localization Opertors.
Fri, 12/11/2009 - 16:01 — SomNambulAuthors: Karlheinz Groechenig, Monika Doerfler
Subjects: Functional Analysis
AbstractWe study families of time-frequency localization operators and derive a new
characterization of modulation spaces. This characterization relates the size
of the localization operators to the global time-frequency distribution. As a
by-product, we obtain a new proof for the existence of multi-window Gabor
frames and extend the structure theory of Gabor frames.Representation and Approximation of Pseudodifferential Operators by Sums of Gabor Multipliers.
Mon, 08/17/2009 - 18:30 — SomNambulAuthors: Karlheinz Groechenig
Subjects: Functional Analysis
AbstractWe investigate a new representation of general operators by means of sums of
shifted Gabor multipliers. These representations arise by studying the matrix
of an operator with respect to a Gabor frame. Each shifted Gabor multiplier
corresponds to a side-diagonal of this matrix. This representation is
especially useful for operators whose associated matrix possesses some
off-diagonal decay. In this case one can completely characterize the symbol
class of the operator by the size of the symbols of the Gabor multipliers.
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