Related papers: Wavefront sets and polarizations on supermanifolds
This is the first in a series of papers laying the foundations for a differential graded approach to derived differential geometry (and other geometries in characteristic zero). In this paper, we study theories of supercommutative algebras…
We start by showing how to approximate unitary and bounded self-adjoint operators by operators in finite dimensional spaces. Using ultraproducts we give a precise meaning for the approximation. In this process we see how the spectral…
We analyse an operator arising in the description of singular solutions to the two-dimensional Keller-Segel problem. It corresponds to the linearised operator in parabolic self-similar variables, close to a concentrated stationary state.…
Superintegrable systems are a class of physical systems which possess more conserved quantities than their degrees of freedom. The study of these systems has a long history and continues to attract significant international attention. This…
As in real microlocal analysis, we prove a Schwartz kernel theorem for $p$-adic distributions. We extend this result for motivic distributions using Cluckers-Loeser's motivic integration. In both settings, we give also a relation between…
A supersymmetric field theory of light diffusion in semi-infinite disordered media is presented. With the help of this technique we justify--at the perturbative level--the local light diffusion proposed by Tiggelen, Lagendijk, and Wiersma…
We study discrete random Schr\"odinger operators via the supersymmetric formalism. We develop a cluster expansion that converges at both strong and weak disorder. We prove the exponential decay of the disorder-averaged Green's function and…
We study generalized polar decompositions of densely defined, closed linear operators in Hilbert spaces and provide some applications to relatively (form) bounded and relatively (form) compact perturbations of self-adjoint, normal, and…
Modeling data using manifold values is a powerful concept with numerous advantages, particularly in addressing nonlinear phenomena. This approach captures the intrinsic geometric structure of the data, leading to more accurate descriptors…
We reformulate superalgebra and supergeometry in completely categorical terms by a consequent use of the functor of points. The increased abstraction of this approach is rewarded by a number of great advantages. First, we show that one can…
We completely characterize $\Delta$- and local subexponentialities of positive-half compound Poisson distributions and extend the characterization on two-sided distributions. Moreover, $\Delta$-subexponentiality of infinitely divisible…
Relating the electromagnetic scattering and absorption properties of an individual particle to the reflection and transmission coefficients of a two-dimensional material composed of these particles is a crucial concept that has driven both…
With this paper we extend our studies [1] on polarized beams by distilling tools from the theory of principal bundles. Four major theorems are presented, one which ties invariant fields with the notion of normal form, one which allows one…
In this paper, we discuss the recognition problem for A_k-type singularities on wave fronts. We give computable and simple criteria of these singularities, which will play a fundamental role in generalizing the authors' previous work "the…
We prove that the distributions defined on the Gelfand-Shilov spaces, and hence more singular than hyperfunctions, retain the angular localizability property. Specifically, they have uniquely determined support cones. This result enables…
In this paper we derive novel families of inclusion sets for the spectrum and pseudospectrum of large classes of bounded linear operators, and establish convergence of particular sequences of these inclusion sets to the spectrum or…
We will present versions of the Rellich-Kondrachov theorem for pseudo-differential operators acting on localizable Hardy spaces. One of the techniques includes boundedness properties for pseudodifferential operators with symbols in the…
We study traveling fronts in a system of one dimensional reaction-diffusion-advection equations motivated by problems in reactive flows. In the limit as a parameter tends to infinity, we construct the approximate front profile and determine…
Working in the time domain, we show that the location of the singularities and the principal symbol of a potential that is conormal to nested submanifolds $S_2 \subset S_1 \subset \mathbb{R}^n$, for $n \geq 3$, can be recovered from the…
In this paper we study the Fourier-Laplace transform of tempered ultrahyperfunctions introduced by Sebasti\~ao e Silva and Hasumi. We establish a generalization of Paley-Wiener-Schwartz theorem for this setting. This theorem is interesting…