542 research outputs found
Weak-Type estimates for the metaplectic representation restricted to the shearing and Dilation subgroup of SL(2, ℝ)
We consider the subgroup G of SL(2, ℝ) consisting of shearing and dilations, and we study the decay at infinity of the matrix coefficients of the metaplectic representation restricted to G. We prove weak-type estimates for such coefficients, which are uniform for functions in the modulation space M 1 . This work represents a continuation of a project aiming at studying weak-type and Strichartz estimates for unitary representations of non-compact Lie groups
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
Metaplectic representation on Wiener amalgam spaces and applications to the Schr\"odinger equation
We study the action of metaplectic operators on Wiener amalgam spaces, giving
upper bounds for their norms. As an application, we obtain new fixed-time
estimates in these spaces for Schr\"odinger equations with general quadratic
Hamiltonians and Strichartz estimates for the Schr\"odinger equation with
potentials
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
The Cauchy Problem for the Vibrating Plate Equation in modulation spaces
The local solvability of the Cauchy problem for the nonlinear vibrating plate
equation is showed in the framework of modulation spaces. In the opposite
direction, it is proved that there is no local wellposedness in Wiener amalgam
spaces even for the solution to the homogeneous vibrating plate equation.Comment: 2 figures, some misprints correcte
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