Related papers: Inequalities for the transformation operators and …
We consider the one-dimensional Schr\"odinger equation with a potential satisfying the standard assumptions of the inverse scattering theory and supported on the half-line $x\ge 0$. For this equation at fixed positive energy we give…
Flag kernels are tempered distributions which generalize these of Calderon-Zygmund type. For any homogeneous group $\mathbb{G}$ the class of operators which acts on $L^{2}(\mathbb{G})$ by convolution with a flag kernel is closed under…
A representation for the kernel of the transmutation operator relating the perturbed Bessel equation with the unperturbed one is obtained in the form of a functional series with coefficients calculated by a recurrent integration procedure.…
Nucleon-nucleon (NN) phase shifts and the spectroscopy of $A \le 6$ nuclei are successfully described by an inverse scattering potential that is separable with oscillator form factors.
The inverse scattering transform is extended to investigate the Tzitz\'{e}ica equation. A set of sectionally analytic eigenfunctions and auxiliary eigenfunctions are introduced. We note that in this procedure, the auxiliary eigenfunctions…
Given a self-adjoint operator H, a self-adjoint trace class operator V and a fixed Hilbert-Schmidt operator F with trivial kernel and co-kernel, using limiting absorption principle an explicit set of full Lebesgue measure is defined such…
By the use of the celebrated Kato's inequality we obtain in this paper some new inequalities for trace class operators on a complex Hilbert space H. Natural applications for functions defined by power series of normal operators are given as…
The method of transfer functions is developed as a tool for studying Bell inequalities, alternative quantum theories and the associated physical properties of quantum systems. Non-negative probabilities for transfer functions result in…
We develop direct and inverse scattering theory for Jacobi operators which are short range perturbations of quasi-periodic finite-gap operators. We show existence of transformation operators, investigate their properties, derive 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…
The matrix Schr\"odinger equation is considered on the half line with the general selfadjoint boundary condition at the origin described by two boundary matrices satisfying certain appropriate conditions. It is assumed that the matrix…
This work aims to bridge the gap between pure and applied research on scalar, linear Volterra equations by examining five major classes: integral and integro-differential equations with completely monotone kernels, such as linear…
We present some reverse Young-type inequalities for the Hilbert-Schmidt norm as well as any unitarily invariant norm. Furthermore, we give some inequalities dealing with operator means. More precisely, we show that if $A, B\in {\mathfrak…
An exact inversion formula for the Lorentz integral transform (LIT) is provided together with the spectrum of the LIT kernel. The exponential increase of the inverse Fourier transform of the LIT kernel entering the inversion formula…
We consider the scattering problem for the nonlinear Schr\"{o}dinger equation with a potential in two space dimensions. Appropriate resolvent estimates are proved and applied to estimate the operator $A(s)$ appearing in commutator…
We study an inverse acoustic scattering problem by the Factorization Method when the unknown scatterer consists of two objects with different physical properties. Especially, we consider the following two cases: One is the case when each…
We analyze two weak random operators, initially motivated from processes in random environment. Intuitively speaking these operators are ill-defined, but using bilinear forms one can deal with them in a rigorous way. This point of view can…
The non-singlet and singlet evolution kernels of the twist--2 light-ray operators for unpolarized and polarized deep inelastic scattering are calculated in $O(\alpha_s)$ for the general case of virtualities $q^2, q'^2 \neq 0$. Special cases…
The S matrix of e--e scattering has the structure of a projection operator that projects incoming separable product states onto entangled two-electron states. In this projection operator the empirical value of the fine-structure constant…
A nonlinear identity for the scattering phase of quantum integrable models is proved.