Some Generalizations of the Hellinger Theorem for Second Order Difference Equations with Matrix Elements
Year: 2013
Type: preprint
Abstract: We obtain several generalizations the Hellinger theorem about $l^2$ solutions of difference equations: instead of second order equations and $ l^2$-solutions, we consider second-order equations with matrix coefficients and their solutions in $l^p,\; 1\le p\le \infty$. In particular it is shown that for a certain class of symmetric difference equations an analog of this theorem holds for $1\le p \le 2$, but it does not hold for $p>2$.
Source: arXiv (Cornell University)
Author: Osipov, A. S.
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2530579596