We consider the dissipative singular q-Sturm-Liouville operators acting in Hilbert space L2 w,q(R+), that extensions of a minimal symmetric operator with deficiency indices (2, 2) (in limit-circle case).We construct self-adjoint dilation and its incoming outgoing spectral representations, which make it possible to determine scattering matrix terms Weyl-Titchmarsh function operator. also functio...

We establish a finite-dimensional version of the Arveson-Stinespring dilation theorem for unital completely positive maps on operator systems. This result can be seen as general principle to deduce theorems from their classical infinite-dimensional counterparts. In addition providing unified proofs known theorems, we versions Agler's rational an annulus, Berger's operators numerical radius at m...

The semi-group of weighted composition operators (Wn)n≥1 whereWnf(z)=(1+z+…+zn−1)f(zn) on the classical Hardy-Hilbert space H2 open unit disk is related to Riemann Hypothesis (RH) (see [16]). semigroup also closely Invariant Subspace Problem (ISP) and Periodic Dilation Completeness (PDCP). We obtain results cyclic vectors, spectra, invariant reducing subspaces. In particular, we show that sever...

critical pulmonary valve stenosis (cpvs) and atrial septal defect (asd) is an uncommon form of congenital heart disease. concurrent transcatheter pulmonary valvuplasty and closure of secundum atrial septal defect appears to be an interesting alternative to surgical correction. we present the simultaneous balloon valvuloplasty of critical pulmonary stenosis (ps) with supra systemic right ventric...

We consider systems of unitary operators on the complex Hilbert space L(R) of the form U :=UDA , v1 ..., vn :=[DT l1 v1 } } } T ln vn : m, l1 , ..., ln # Z], where DA is the unitary operator corresponding to dilation by an n_n real invertible matrix A and Tv1 , ..., Tvn are the unitary operators corresponding to translations by the vectors in a basis [v1 , ..., vn] for R. Orthonormal wavelets a...

Mathematical morphology is a very successful branch of image processing with a history of more than four decades. Its fundamental operations are dilation and erosion, which are based on the notion of a maximum and a minimum with respect to an order. Many operators constructed from dilation and erosion are available for grey value images, and recently useful analogs of these processes for matrix...

on utilizing the spectral representation of selfadjoint operators in hilbert spaces, some error bounds in approximating $n$-time differentiable functions of selfadjoint operators in hilbert spaces via a taylor's type expansion are given.

In this paper we use concepts from the lattice-based theory of morphological operators and fuzzy sets to develop generalized lattice image operators that can be expressed as nonlinear convolutions that are suprema or infima of fuzzy intersection or union norms. Our emphasis (and differences with previous works) is the construction of pairs of fuzzy dilation and erosion operators that form latti...

achalasia is a well- defined esophageal motor disorder. graded pneumatic dilation using rigiflex ballon is one of the therapeutic modalities that had not been evaluated in a large long-term study. we aimed at evaluating long-term efficacy of graded rigiflex pneumatic dilation in the treatment of achalasia. symptomatic patients with achalasia who had been referred to our center were consecutivel...