Separation problem for the Grushin differential operator in Banach spaces


Atia, H. A.


Abstract

carpathian_2014_30_1_031_037_abstract

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).

Additional Information

Author(s)

Atia, H. A.