1,132 research outputs found
Sharpness of some properties of Wiener amalgam and modulation spaces
We prove sharp estimates for the dilation operator , when acting on Wiener amalgam spaces . Scaling arguments are
also used to prove the sharpness of the known convolution and pointwise
relations for modulation spaces , as well as the optimality of an
estimate for the Schr\"odinger propagator on modulation spaces.Comment: 12 page
Time-frequency Analysis of Born-Jordan Pseudodifferential Operators
Born-Jordan operators are a class of pseudodifferential operators arising as
a generalization of the quantization rule for polynomials on the phase space
introduced by Born and Jordan in 1925. The weak definition of such operators
involves the Born-Jordan distribution, first introduced by Cohen in 1966 as a
member of the Cohen class. We perform a time-frequency analysis of the Cohen
kernel of the Born -Jordan distribution, using modulation and Wiener amalgam
spaces. We then provide sufficient and necessary conditions for Born-Jordan
operators to be bounded on modulation spaces. We use modulation spaces as
appropriate symbols classes.Comment: 21 pages, 1 figur
Pseudodifferential operators on , Wiener amalgam and modulation spaces
We give a complete characterization of the continuity of pseudodifferential
operators with symbols in modulation spaces , acting on a given
Lebesgue space . Namely, we find the full range of triples , for
which such a boundedness occurs. More generally, we completely characterize the
same problem for operators acting on Wiener amalgam space and even
on modulation spaces . Finally the action of pseudodifferential
operators with symbols in W(\Fur L^1,L^\infty) is also investigated.Comment: 27 page
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