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Discreteness of the Spectrum for Some Differential Operators With Unbounded Coefficients in R^n
"... We give sufficient conditions for the discreteness of the spectrum of differential operators of the form Au = \Gamma\Deltau +hrF;rui in L 2 (R n ) where d(x) = e \GammaF (x) dx and for Schrödinger operators in L 2 (R n ). Our conditions are also necessary in the case of polynomial coeffic ..."
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We give sufficient conditions for the discreteness of the spectrum of differential operators of the form Au = \Gamma\Deltau +hrF;rui in L 2 (R n ) where d(x) = e \GammaF (x) dx and for Schrödinger operators in L 2 (R n ). Our conditions are also necessary in the case of polynomial coefficients.
L^pRegularity for Elliptic Operators with Unbounded Coefficients
, 2002
"... Under suitable conditions on the functions a 2 C N 2 ), F 2 C ), and V : R [0; 1), we show that the operator Au = r(aru) + F ru V u with domain W V (R ) = fu 2 ) : V u 2 L )g generates a positive analytic semigroup on L ), 1 < p < 1. ..."
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Under suitable conditions on the functions a 2 C N 2 ), F 2 C ), and V : R [0; 1), we show that the operator Au = r(aru) + F ru V u with domain W V (R ) = fu 2 ) : V u 2 L )g generates a positive analytic semigroup on L ), 1 < p < 1.
The Domain of the OrnsteinUhlenbeck Operator on an L^pSpace with Invariant Measure
, 2001
"... We show that the domain of the OrnsteinUhlenbeck operator on ; dx) equals the weighted Sobolev space W ; dx), where dx is the corresponding invariant measure. Our approach relies on the operator sum method, namely the commutative and the non commutative DoreVenni theorems. ..."
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We show that the domain of the OrnsteinUhlenbeck operator on ; dx) equals the weighted Sobolev space W ; dx), where dx is the corresponding invariant measure. Our approach relies on the operator sum method, namely the commutative and the non commutative DoreVenni theorems.