相关论文: Discrete Wave-front sets of Fourier Lebesgue and m…
We establish sharp convolution and multiplication estimates in weighted Lebesgue, Fourier Lebesgue and modulation spaces. Especially we recover some known results.
In this paper, we give characterizations of usual wave front set and Sobolev type wave front set in terms of wave packet transform without any restriction on basic wave packet.
In this paper, we characterize the wave front sets of solutions to fractional Schr\"{o}dinger equations \(i\partial_{t}u =(-\Delta)^{\theta/2}u + V(x)u\) with $0<\theta <2$ via the wave packet transform (short-time Fourier transform). We…
We give some new results related to the directional short-time Fourier transform (DSTFT) and extend them on the spaces $\mathcal K_{1}(\mathbb R^{n})$ and $\mathcal K_{1}({\mathbb R})\widehat{\otimes}\mathcal U(\mathbb C^n)$ and their…
In recent years directional multiscale transformations like the curvelet- or shearlet transformation have gained considerable attention. The reason for this is that these transforms are - unlike more traditional transforms like wavelets -…
A generalized notion of oscillatory integrals that allows for inhomogeneous phase functions of arbitrary positive order is introduced. The wave front set of the resulting distributions is characterized in a way that generalizes the…
We characterize the wave front set $WF^P_\ast(u)$ with respect to the iterates of a linear partial differential operator with constant coefficients of a classical distribution $u\in{\mathcal D}'(\Omega)$, $\Omega$ an open subset in…
The concept of wave front set was introduced in 1969-1970 by M. Sato in the hyperfunctions context and by L. H\"ormander in the $\mathcal C^{\infty}$ context. Howe used the theory of wave front sets in the study of Lie groups…
We define and prove some properties of the semi-classical wavefront set. We also define and study semi-classical Fourier integral operators, of which we give a complete characterization. Lastly, we prove a generalization of the…
We propose a criterion for the existence of monotone wavefronts in non-monotone and non-local monostable diffusive equations of the Mackey-Glass type. This extends recent results by Gomez et al proved for the particular case of equations…
In this paper we prove the convergence of solutions to discrete models for binary waveguide arrays toward those of their formal continuum limit, for which we also show the existence of localized standing waves. This work rigorously…
In this paper, we determine the C-infinity type wave front sets of the solutions to the Schrodinger equations with time-dependent variable coefficients and potentials by using the wave packet transform. We introduce the infinite sum and…
We give a definition of `coherent tangent bundles', which is an intrinsic formulation of wave fronts. In our application of coherent tangent bundles for wave fronts, the first fundamental forms and the third fundamental forms are considered…
We propose the set of coupled ordinary differential equations dn_j/dt=(n_{j-1})^2-(n_j)^2 as a discrete analog of the classic Burgers equation. We focus on traveling waves and triangular waves, and find that these special solutions of the…
We show that the results of [BM97, DeB02b, Oka, Lus85, AA07, Tay16] imply a positive answer to the question of Moeglin-Waldspurger on wave-front sets in the case of depth zero cuspidal representations. Namely, we deduce that for large…
A new theory of edge waves over a slowly varying depth.
We give a short introduction to discrete flat fronts in hyperbolic space and prove that any discrete flat front in the mixed area sense admits a Weierstrass representation.
We study wave-front sets of representations of reductive groups over global or non-archimedean local fields.
We compute the stable wave front set of theta representations for certain tame Brylinski-Deligne covers of a connected reductive $p$-adic group. The computation involves two main inputs. First we use a theorem of Okada, adapted to covering…
The aim of this exposition is to explain basic ideas behind the concept of diffusive wavelets on spheres in the language of representation theory of Lie groups and within the framework of the group Fourier transform given by Peter-Weyl…