Displaying similar documents to “On positive Rockland operators”

Lipschitz continuity of densities of stable semigroups of measures

Paweł Głowacki (1993)

Colloquium Mathematicae

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In this paper we raise the question of regularity of the densities h t of a symmetric stable semigroup μ t of measures on the homogeneous group N under the mere assumption that the densities exist. (For a criterion of the existence of the densities of such semigroups see [11].)

A nilpotent Lie algebra and eigenvalue estimates

Jacek Dziubański, Andrzej Hulanicki, Joe Jenkins (1995)

Colloquium Mathematicae

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The aim of this paper is to demonstrate how a fairly simple nilpotent Lie algebra can be used as a tool to study differential operators on ℝ n with polynomial coefficients, especially when the property studied depends only on the degree of the polynomials involved and/or the number of variables.

Asymptotic behaviour of a transport equation

Ryszard Rudnicki (1992)

Annales Polonici Mathematici

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We study the asymptotic behaviour of the semigroup of Markov operators generated by the equation u t + b u x + c u = a ∫ 0 a x u ( t , a x - y ) μ ( d y ) . We prove that for a > 1 this semigroup is asymptotically stable. We show that for a ≤ 1 this semigroup, properly normalized, converges to a limit which depends only on a.

Spectral properties of non-self-adjoint operators

Johannes Sjöstrand (2009)

Journées Équations aux dérivées partielles

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This text contains a slightly expanded version of my 6 hour mini-course at the PDE-meeting in Évian-les-Bains in June 2009. The first part gives some old and recent results on non-self-adjoint differential operators. The second part is devoted to recent results about Weyl distribution of eigenvalues of elliptic operators with small random perturbations. Part III, in collaboration with B. Helffer, gives explicit estimates in the Gearhardt-Prüss theorem for semi-groups.

Decomposition and disintegration of positive definite kernels on convex *-semigroups

Jan Stochel (1992)

Annales Polonici Mathematici

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The paper deals with operator-valued positive definite kernels on a convex *-semigroup whose Kolmogorov-Aronszajn type factorizations induce *-semigroups of bounded shift operators. Any such kernel Φ has a canonical decomposition into a degenerate and a nondegenerate part. In case is commutative, Φ can be disintegrated with respect to some tight positive operator-valued measure defined on the characters of if and only if Φ is nondegenerate. It is proved that a representing measure of...