In some recent works on scattering theory [KR1, KR2, KR3, KR5], it was conjectured and then proved that, modulo a compact term, the wave operators for Schrödinger systems can be rewritten as a product of a function of the dilation operator A and a function of the Laplacian −∆. Furthermore, the functions of the dilation operator are rather insensitive to a particular choice of the perturbed oper...

‎In this manuscript‎, ‎we study various by uniqueness results for inverse spectral problems of Sturm--Liouville operators using three spectrum with a finite number of discontinuities at interior points which we impose the usual transmission conditions‎. ‎We consider both the cases of classical Robin and eigenparameter dependent boundary conditions.

The application of mathematical morphology to image processing and analysis has initiated a new approach for solving a number of problems in the image enhancement field. So, we have used morphological operators to detect and extract the background of images. Various operators used are erosion, dilation, opening and closing. After the background is extracted, contrast of bad lightning image is i...

We investigate how common binary mathematical morphology operators can be adapted so that the size of the structuring element can vary across the image pixels. We show that when the structuring elements are balls of a metric, locally adaptable erosion and dilation can be efficiently implemented as a variant of distance transformation algorithms. Opening and closing are obtained by a local thres...

A traditional wavelet is a special case of a vector in a separable Hilbert space that generates a basis under the action of a system of unitary operators defined in terms of translation and dilation operations. A Coxeter/fractal-surface wavelet is obtained by defining fractal surfaces on foldable figures, which tesselate the embedding space by reflections in their bounding hyperplanes instead o...

We study the Classical Probability analogue of the dilations of a quantum dynamical semigroup in Quantum Probability. Given a (not necessarily homogeneous) Markov chain in discrete time in a finite state space E, we introduce a second system, an environment, and a deterministic invertible time-homogeneous global evolution of the system E with this environment such that the original Markov evolu...