Fundamental solutions for a class of non-elliptic homogeneous differential operators

A Class of compact operators on homogeneous spaces

Let  $varpi$ be a representation of the homogeneous space $G/H$, where $G$ be a locally compact group and  $H$ be a compact subgroup of $G$. For  an admissible wavelet $zeta$ for $varpi$  and $psi in L^p(G/H), 1leq p <infty$, we determine a class of bounded  compact operators  which are related to continuous wavelet transforms on homogeneous spaces and they are called localization operators.

On the fundamental solutions of a class of elliptic quartic operators in dimension 3

The (uniquely determined) even and homogeneous fundamental solutions of the linear elliptic partial differential operators with constant coefficients of the form ∑3 j=1 ∑3 k=1 cjk∂ j ∂2 k are represented by elliptic integrals of the first kind. Thereby we generalize Fredholm’s example ∂4 1 +∂4 2 +∂4 3 , which, up to now, was the only irreducible homogeneous quartic operator in 3 variables the f...

On the Spectral Properties of Degenerate Non-selfadjoint Elliptic systems of Differential Operators

Existence of ground state solutions for a class of nonlinear elliptic equations with fast increasing weight

‎This paper is devoted to get a ground state solution for a class of nonlinear elliptic equations with fast increasing weight‎. ‎We apply the variational methods to prove the existence of ground state solution‎.

a class of compact operators on homogeneous spaces

let  $varpi$ be a representation of the homogeneous space $g/h$, where $g$ be a locally compact group and  $h$ be a compact subgroup of $g$. for  an admissible wavelet $zeta$ for $varpi$  and $psi in l^p(g/h), 1leq p