Related papers: Wave fronts and (almost) free divisors
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 generalize our previous linear result [1] in obtaining gravitational waves from our piecewise flat model for gravity in 3+1 dimensions to exact piecewise flat configurations describing exact planar gravitational waves. We show explicitly…
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…
Pinning and depinning of wavefronts are ubiquitous features of spatially discrete systems describing a host of phenomena in physics, biology, etc. A large class of discrete systems is described by overdamped chains of nonlinear oscillators…
This work discusses modons, or dipolar vortices, propagating along sloping topography. Two different regimes exist which are studied separately using the surface quasi-geostrophic equations. First, when the modon propagates in the opposite…
We characterize singularities of focal surfaces of wave fronts in terms of differential geometric properties of the initial wave fronts. Moreover, we study relationships between geometric properties of focal surfaces and geometric…
Let G be a special orthogonal group SO(2n+1) defined over a p-adic field F. Let $\pi$ be an admissible irreducible representation of G(F) which is tempered and of unipotent reduction. We prove that $\pi$ has a wave front set. In some…
It is well known that the classical and Sobolev wave fronts were extended into non-equivalent global versions by the use of the short-time Fourier transform. In this very short paper we give complete characterisations of initial wave front…
Continuing our recent work we study polynomial masks of multivariate tight wavelet frames from two additional and complementary points of view: convexity and system theory. We consider such polynomial masks that are derived by means of the…
We obtain discrete characterizations of wave front sets of Fourier-Lebesgue and quasianalytic type. It is shown that the microlocal properties of an ultradistribution can be obtained by sampling the Fourier transforms of its localizations…
Wave front propagation with non-trivial bottom topography is studied within the formalism of hyperbolic long wave models. Evolution of non-smooth initial data is examined, and in particular the splitting of singular points and their short…
In this paper, we present a semiclassical description of surface waves or modes in an elastic medium near a boundary, in spatial dimension three. The medium is assumed to be essentially stratified near the boundary at some scale comparable…
One deals with arbitrary reduced free divisors in a polynomial ring over a field of characteristic zero, by stressing the ideal theoretic and homological behavior of the corresponding singular locus. A particular emphasis is given to both…
We develop a polynomial basis to be used in numerical calculations of light-front Fock-space wave functions. Such wave functions typically depend on longitudinal momentum fractions that sum to unity. For three particles, this constraint…
In this expository note we present an introduction to the Gabor wave front set. As is often the case, this tool in microlocal analysis has been introduced and reinvented in different forms which turn out to be equivalent or intimately…
The increasing use of freeform optical surfaces raises the demand for optical design tools developed for generalized systems. In the design process surface-by-surface aberration contributions are of special interest. The expansion of the…
We present a new topological method to study the discriminantal loci of an algebraic variety defined in a product of projective spaces. Our approach relies on an efficient use of groupoid to describe the monodromy. As an example, we treat…
We study focal surfaces of (wave) fronts associated to unbounded principal curvatures near non-degenerate singular points of initial fronts. We give characterizations of singularities of those focal surfaces in terms of types of…
We review and extend the description of ultradifferentiable functions by their almost analytic extensions, i.e., extensions to the complex domain with specific vanishing rate of the $\bar \partial$-derivative near the real domain. We work…
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…