carpathian_2014_30_1_031_037_001

Separation problem for the Grushin differential operator in Banach spaces

Atia, H. A.

Abstract

carpathian_2014_30_1_031_037_abstract

Issue no: Vol 30/2014 no. 1 Tags: Banach space, Separation, Grushin differential operator, Operator potential

Description
Additional information

Our goal in this work is to study the separation problem for the Grushin differential operator formed by

$\begin{equation*}Gu=-\frac{1}{2}\left( \frac{\partial ^{2}u}{\partial x^{2}}+\frac{x^{4}}{4}\frac{\partial ^{2}u}{\partial y^{2}}\right) +Q(x,y)u(x,y),\,\forall \(x,y)\in R^{2},\,\,\end{equation*}$

in the Banach space $H_{1}(R^{2}),$ where the potential $Q(x,y)\in L(\ell_{1}),$ is a bounded linear operator which transforms at $\ell _{1}$ invalue of $(x,y).$

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Author(s)	Atia, H. A.