arXiv subjects

S. Torba

Publications and source records attributed to S. Torba.

4 recordsLinked to original sources

arXiv2008

Inverse theorems in the theory of approximation of vectors in a Banach space with exponential type entire vectors

Arbitrary operator A on a Banach space X which is the generator of C_0-group with certain growth condition at infinity is considered. The relationship between its exponential type entire vectors and its spectral subspaces is found. Inverse theorems on connection between the degree of smoothness of vector $x\in X$ with respect to operator A, the rate of convergence to zero of the best approximation of x by exponential type entire vectors for operator A, and the k-module of continuity are established. Also, a generalization of the Bernstein-type inequality is obtained. The results allow to obtain Bernstein-type inequalities in weighted L_p spaces.

math.FA↗

arXiv2008

Direct Theorems in the Theory of Approximation of the Banach Space Vectors by Entire Vectors of Exponential Type

For an arbitrary operator A on a Banach space X which is a generator of C_0-group with certain growth condition at the infinity, the direct theorems on connection between the smoothness degree of a vector $x\in X$ with respect to the operator A, the order of convergence to zero of the best approximation of x by exponential type entire vectors for the operator A, and the k-module of continuity are given. Obtained results allows to acquire Jackson-type inequalities in many classic spaces of periodic functions and weighted $L_p$ spaces.

math.FA↗

arXiv2007

p-Adic Schr\"{o}dinger-Type Operator with Point Interactions

A $p$-adic Schr\"{o}dinger-type operator $D^{\alpha}+V_Y$ is studied. $D^{\alpha}$ ($\alpha>0$) is the operator of fractional differentiation and $V_Y=\sum_{i,j=1}^nb_{ij}<\delta_{x_j}, \cdot>\delta_{x_i}$ $(b_{ij}\in\mathbb{C})$ is a singular potential containing the Dirac delta functions $\delta_{x}$ concentrated on points $\{x_1,...,x_n\}$ of the field of $p$-adic numbers $\mathbb{Q}_p$. It is shown that such a problem is well-posed for $\alpha>1/2$ and the singular perturbation $V_Y$ is form-bounded for $\alpha>1$. In the latter case, the spectral analysis of $\eta$-self-adjoint operator realizations of $D^{\alpha}+V_Y$ in $L_2(\mathbb{Q}_p)$ is carried out.

math-ph↗

arXiv2006

p-Adic Fractional Differentiation Operator with Point Interactions

Finite rank point perturbations of the $p$-adic fractional differentiation operator $D^α$ are studied. The main attention is paid to the description of operator realizations (in $L_2(\mathbb{Q}_p)$) of the heuristic expression $D^α+\sum_{i,j=1}^{n}b_{ij}<δ_{x_j}, \cdot>δ_{x_i}$ in a form that is maximally adapted for the preservation of physically meaningful relations to the parameters $b_{ij}$ of the singular potential.

math-ph↗