eigenfunctions of an globally hypoelliptic operator
$begingroup$
An operator $L$ is said globally hypoelliptic in the Schwartz space $mathcal{S}(Bbb{R}^{n})$ if $uin mathcal{S}'(Bbb{R}^{n}), Luin mathcal{S}(Bbb{R}^{n})Rightarrow uin mathcal{S}(Bbb{R}^{n})$
where $mathcal{S}'(Bbb{R}^{n})$ is the space of all tempered distributions.
Let $uin L^p(Bbb{R}^{n})$ an eigenfunction of $L$ i,e., $Lu=au$ with $ain Bbb{R}$.
Can we say that $uin mathcal{S}(Bbb{R}^{n})$?
pde regularity-theory-of-pdes elliptic-operators
asked Dec 23 '18 at 18:45
KacdimaKacdima
566
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add a comment |
$begingroup$
An operator $L$ is said globally hypoelliptic in the Schwartz space $mathcal{S}(Bbb{R}^{n})$ if $uin mathcal{S}'(Bbb{R}^{n}), Luin mathcal{S}(Bbb{R}^{n})Rightarrow uin mathcal{S}(Bbb{R}^{n})$
where $mathcal{S}'(Bbb{R}^{n})$ is the space of all tempered distributions.
Let $uin L^p(Bbb{R}^{n})$ an eigenfunction of $L$ i,e., $Lu=au$ with $ain Bbb{R}$.
Can we say that $uin mathcal{S}(Bbb{R}^{n})$?
pde regularity-theory-of-pdes elliptic-operators
asked Dec 23 '18 at 18:45
KacdimaKacdima
566
$endgroup$
add a comment |
$begingroup$
An operator $L$ is said globally hypoelliptic in the Schwartz space $mathcal{S}(Bbb{R}^{n})$ if $uin mathcal{S}'(Bbb{R}^{n}), Luin mathcal{S}(Bbb{R}^{n})Rightarrow uin mathcal{S}(Bbb{R}^{n})$
where $mathcal{S}'(Bbb{R}^{n})$ is the space of all tempered distributions.
Let $uin L^p(Bbb{R}^{n})$ an eigenfunction of $L$ i,e., $Lu=au$ with $ain Bbb{R}$.
Can we say that $uin mathcal{S}(Bbb{R}^{n})$?
pde regularity-theory-of-pdes elliptic-operators
asked Dec 23 '18 at 18:45
KacdimaKacdima
566
$endgroup$
An operator $L$ is said globally hypoelliptic in the Schwartz space $mathcal{S}(Bbb{R}^{n})$ if $uin mathcal{S}'(Bbb{R}^{n}), Luin mathcal{S}(Bbb{R}^{n})Rightarrow uin mathcal{S}(Bbb{R}^{n})$
where $mathcal{S}'(Bbb{R}^{n})$ is the space of all tempered distributions.
Let $uin L^p(Bbb{R}^{n})$ an eigenfunction of $L$ i,e., $Lu=au$ with $ain Bbb{R}$.
Can we say that $uin mathcal{S}(Bbb{R}^{n})$?
pde regularity-theory-of-pdes elliptic-operators
pde regularity-theory-of-pdes elliptic-operators
asked Dec 23 '18 at 18:45
KacdimaKacdima
566
asked Dec 23 '18 at 18:45
KacdimaKacdima
566
asked Dec 23 '18 at 18:45
KacdimaKacdima
566
asked Dec 23 '18 at 18:45
KacdimaKacdima
566
asked Dec 23 '18 at 18:45
KacdimaKacdima
566
566
add a comment |
add a comment |
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