-spectrum of Ornstein-Uhlenbeck operators
-convergence of Bernstein-Kantorovich-type operators
We study a Kantorovich-type modification of the operators introduced in [1] and we characterize their convergence in the -norm. We also furnish a quantitative estimate of the convergence.
Discreteness of the spectrum for some differential operators with unbounded coefficients in
We give sufficient conditions for the discreteness of the spectrum of differential operators of the form in where and for Schrödinger operators in . Our conditions are also necessary in the case of polynomial coefficients.
On the three-space property for locally convex spaces.
The domain of the Ornstein-Uhlenbeck operator on an -space with invariant measure
We show that the domain of the Ornstein-Uhlenbeck operator on equals the weighted Sobolev space , where is the corresponding invariant measure. Our approach relies on the operator sum method, namely the commutative and the non commutative Dore-Venni theorems.
An elementary proof of asymptotic behavior of solutions of U" = VU
We provide an elementary proof of the asymptotic behavior of solutions of second order differential equations without successive approximation argument.
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