Related papers: On Generalizations of the Nonwindowed Scattering T…
Continuous wavelet transforms arising from the quasiregular representation of a semidirect product of a vector group with a matrix group -- the so-called dilation group -- have been studied by various authors. Recently the attention has…
The nondecimated or translation-invariant wavelet transform (NDWT) is a central tool in classical multiscale signal analysis, valued for its stability, redundancy, and shift invariance. This paper develops two complementary quantum…
We offer a consistent dynamical formulation of stationary scattering in two and three dimensions that is based on a suitable multidimensional generalization of the transfer matrix. This is a linear operator acting in an infinite-dimensional…
The covariantization procedure is usually referred to the translation operator, that is the derivative. Here we introduce a general method to covariantize arbitrary differential operators, such as the ones defining the fundamental group of…
In this paper, we exploit the theory of convolution of index Whittaker transform for study of continuous and discrete Index Whittaker wavelet transform and discuss some of its basic properties. Certain boundedness, Plancherel as well as…
We consider the problem of characterizing the Sobolev wavefront set of a tempered distribution $u\in\mathcal{S}'(\mathbb{R}^{d})$ in terms of its continuous wavelet transform, with the latter being defined with respect to a suitably chosen…
We prove new and explicit formulas for the wave operators of Schroedinger operators in R^3. These formulas put into light the very special role played by the generator of dilations and validate the topological approach of Levinson's theorem…
The construction of generalized continuous wavelet transforms on locally compact abelian groups $A$ from quasi-regular representations of a semidirect product group $G = A \rtimes H$ acting on ${\rm L}^2(A)$ requires the existence of a…
The purpose of this paper is to establish a geometric scattering result for a conformally invariant nonlinear wave equation on an asymptotically simple spacetime. The scattering operator is obtained via trace operators at null infinities.…
Using Dunkl operators, we introduce a continuous family of canonical invariants of finite reflection groups. We verify that the elementary canonical invariants of the symmetric group are deformations of the elementary symmetric polynomials.…
We prove global Sobolev regularity and pointwise upper bounds for the gradient of transition densities associated with second order differential operators in $\mathbb{R}^d$ with unbounded diffusion, drift and potential terms.
A recognized trend of research investigates generalizations of the Hadamard's inversion theorem to functions that may fail to be differentiable. In this vein, the present paper explores some consequences of a recent result about the…
We develop direct and inverse scattering theory for Jacobi operators (doubly infinite second order difference operators) with steplike coefficients which are asymptotically close to different finite-gap quasi-periodic coefficients on…
We show that an inverse scattering problem for a semilinear wave equation can be solved on a manifold having an asymptotically Minkowskian infinity, that is, scattering functionals determine the topology, differentiable structure, and the…
The symplectic wavelet transformation [Opt. Lett. 31 (2006) 3432], which is related to quantum optical Fresnel transform, is developed to the symplectic-dilation mixed wavelet transform (SDWT). The SDWT involves both a real-variable…
We extend the invariance principle for a characteristic function of a dissipative operator with respect to the group of affine transformations of the real axis preserving the orientation to the case of general $SL_2(\bbR)$ transformations.
Let F be a closed non-orientable surface. We classify all finite order invariants of immersions of F into R^3, with values in any Abelian group. We show they are all functions of the universal order 1 invariant that we construct as T \oplus…
We generalize the non-linear one-dimensional equation of a fluid layer for any depth and length as an infinite order differential equation for the steady waves. This equation can be written as a q-differential one, with its general solution…
In this paper, we extend the concept of continuous Bessel wavelet transform in $L^p$-space and derived the Parseval's as well as the inversion formulas. By using Bessel wavelet coefficients we characterized the Besov- Hankel space.
We obtain a formula for the Schwartz kernel of the scattering operator in terms of the Schwartz kernel of the fundamental solution of the wave operator on asymptotically hyperbolic manifolds. If there are no trapped geodesics, this formula…