Some remarks on degenerate hypoelliptic Ornstein–Uhlenbeck operators

Some Remarks on Degenerate Hypoelliptic Ornstein-uhlenbeck Operators

We study degenerate hypoelliptic Ornstein-Uhlenbeck operators in L spaces with respect to invariant measures. The purpose of this article is to show how recent results on general quadratic operators apply to the study of degenerate hypoelliptic Ornstein-Uhlenbeck operators. We first show that some known results about the spectral and subelliptic properties of Ornstein-Uhlenbeck operators may be...

Degenerate Hypoelliptic Operators and the Gaussian Kernel

Spectral Properties of Hypoelliptic Operators

We study hypoelliptic operators with polynomially bounded coefficients that are of the form K = ∑m i=1 X i Xi + X0 + f , where the Xj denote first order differential operators, f is a function with at most polynomial growth, and X i denotes the formal adjoint of Xi in L. For any ε > 0 we show that an inequality of the form ‖u‖δ,δ ≤ C(‖u‖0,ε + ‖(K + iy)u‖0,0) holds for suitable δ and C which are...

Some Remarks about Almost Semi-hyponormal Operators

We define the class of almost semi-hyponormal operators on a Hilbert space and provide some sufficient conditions in which such operators are almost normal, that is their self-commutator is in the trace-class. Mathematics Subject Classification: 47B20

Some Remarks on the Invariant Subspace Problem for Hyponormal Operators

We make some remarks concerning the invariant subspace problem for hyponormal operators. In particular, we bring together various hypotheses that must hold for a hyponormal operator without nontrivial invariant subspaces, and we discuss the existence of such operators. 2000 Mathematics Subject Classification. 47B20, 47A15. Let be a separable, infinite-dimensional, complex Hilbert space and deno...