Related papers: Inequalities for the transformation operators and …
There have been many proposed forms of fractional calculus, which can be grouped into a few broad classes of operators. By replacing the kernel of the power function with another kernel function, the traditional Riemann-Liouville formula…
We prove weighted strong inequalities for the multilinear potential operator ${\cal T}_{\phi}$ and its commutator, where the kernel $\phi$ satisfies certain growth condition. For these operators we also obtain Fefferman-Stein type…
We establish a set of relations between several quite diverse types of weighted inequalities involving various integral operators and fairly general quasinorm-like functionals which we call sub-monotone. The main result enables one to solve…
A self-contained discussion of integral equations of scattering is presented in the case of centrally-symmetric potentials in one dimension, which will facilitate the understanding of more complex scattering integral equations in two and…
The question of complete integrability of evolution equations associated to $n\times n$ first order isospectral operators is investigated using the inverse scattering method. It is shown that for $n>2$, e.g. for the three-wave interaction,…
An approximate inverse scattering method [7,8] has been used to construct separable potentials with the Laguerre form factors. As an application, we invert the phase shifts of proton-proton in the $^1S_0$ and $^3P_2-^3F_2$ channels and…
In this paper, we give a detailed survey on norm inequalities for inner product type integral transformers. We first consider unitarily invariant norms and operator valued functions. We then give results on norm inequalities for inner…
Necessary and sufficient conditions are given for the similarity between two perturbations of the (backward) shift by rank one operators, under certain assumptions on the perturbations. The proof of similarity is based on an explicit…
We study a family of convolution operators whose kernels have a singularity on the unit sphere. As a result, we prove the regarding L^p-L^q Sobolev inequalities.
The inverse scattering transform for the focusing nonlinear Schrodinger equation is presented for a general class of initial conditions whose asymptotic behavior at infinity consists of counterpropagating waves. The formulation takes into…
The inverse scattering problem of the three-dimensional Schroedinger equation is considered at fixed scattering energy with spherically symmetric potentials. The phase shifts determine the potential therefore a constructive scheme for…
We characterize those homogeneous translation invariant symmetric non-local operators with positive maximum principle whose harmonic functions satisfy Harnack's inequality. We also estimate the corresponding semigroup and the potential…
The information content and properties of the cross section for atom scattering from a defect on a flat surface are investigated. Using the Sudden approximation, a simple expression is obtained that relates the cross section to the…
In this article, we conduct a study of integral operators defined in terms of non-convolution type kernels with singularities of various degrees. The operators that fall within our scope of research include fractional integrals, fractional…
In this paper we introduce a new technique for proving norm inequalities in operator ideals with an unitarily invariant norm. Among the well known inequalities which can be proved with this technique are the L\"owner-Heinz inequality,…
We give a general formulation of Jensen's operator inequality for unital fields of positive linear mappings, and we consider different types of converse inequalities.
We present a method to reconstruct the dielectric susceptibility (scattering potential) of an inhomogeneous scattering medium, based on the solution to the inverse scattering problem with internal sources. We employ the theory of…
The numerical algorithm of the inverse quantum scattering is developed. This algorithm is based on the Marchenko theory, and includes three steps. The first one is the algebraic Pade approximation of the unitary S-matrix, what is realized…
We consider the $\alpha$-sine transform of the form $T_\alpha f(y)=\int_0^\infty\vert\sin(xy)\vert^\alpha f(x)dx$ for $\alpha>-1$, where $f$ is an integrable function on $\mathbb{R}_+$. First, the inversion of this transform for $\alpha>1$…
For the direct problem, we give the asymptotic distribution of the (real and non-real) transmission eigenvalues for the Schrodinger operator on the half line. For the inverse problem, we prove that the potential can be uniquely determined…