相关论文: The character and the wave front set correspondenc…
Given a real irreducible dual pair there is an integral kernel operator which maps the distribution character of an irreducible admissible representation of the group with the smaller or equal rank to an invariant eigendistribution on the…
In this paper it is shown that the wave front set of a direct integral of singular, irreducible representations of a real, reductive algebraic group is contained in the singular set. Combining this result with the results of the first paper…
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…
We introduce discrete wave-front sets with respect to Fourier Lebesgue and modulation spaces. We prove that these wave-front sets agree with corresponding wave-front sets of "continuous type".
We consider Schr\"odinger equations with variable coefficients and the harmonic potential. We suppose the perturbation is short-range type in the sense of [Nakamura 2004]. We characterize the wave front set of the solutions to the equation…
The wavefront set is a fundamental invariant of an admissible representation arising from the Harish-Chandra-Howe local character expansion. In this paper, we give a precise formula for the wavefront set of an irreducible representation of…
In this second paper of a series dedicated to type I Howe duality for finite fields, we explicitly describe the eta and zeta correspondences constructed in the first paper in terms of G. Lusztig's parametrization of the irreducible…
In this paper we extend some results from our earlier papers on wave-front sets, concerning wave-front sets of Fourier-Lebesgue and modulation space types, to a broader class of spaces of ultradistributions, and relate these wave-front sets…
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…
If $G$ is a Lie group, $H\subset G$ is a closed subgroup, and $\tau$ is a unitary representation of $H$, then the authors give a sufficient condition on $\xi\in i\mathfrak{g}^*$ to be in the wave front set of $\operatorname{Ind}_H^G\tau$.…
We study convective stability of a two-front superposition in a reaction-diffusion system. Due to the instability of the connecting equilibrium, long-range semi-strong interaction is expected between the two waves. When restricting to the…
We consider a reaction-diffusion equation in a one-dimensional space, where the diffusion coefficient changes sign from positive to negative and back to positive. The reaction term is bistable, with its interior zero located in the region…
The wavefront set is a fundamental invariant arising from the Harish-Chandra-Howe local character expansion of an admissible representation. We prove a precise formula for the wavefront set of an irreducible Iwahori-spherical representation…
We study the planar front solution for a class of reaction diffusion equations in multidimensional space in the case when the essential spectrum of the linearization in the direction of the front touches the imaginary axis. At the linear…
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…
Vogan and Barbasch-Vogan attach two similar invariants to representations of a reductive Lie group, one by an algebraic process, the other analytic. They conjectured that the two invariants determine each other in a definite manner. Here we…
We develop a comprehensive theory of the stable representation categories of several sequences of groups, including the classical and symmetric groups, and their relation to the unstable categories. An important component of this theory is…
We calculate certain estimates for the solution of the characteristic problem of the wave equation reduced to first order, in terms of the free data prescribed on two transverse surfaces, one of which is characteristic. Estimates of such…
We consider a reaction-diffusion equation in narrow random channels. We approximate the generalized solution to this equation by the corresponding one on a random graph. By making use of large deviation analysis we study the asymptotic wave…
We introduce the wave-front set for distributions with respect to Fourier images of weighted translation invariant Banach function spaces. We prove that usual mapping properties for pseudo-differential operators hold in the context of such…