A note on Schrödinger operators with polynomial potentials

Jacek Dziubański

Displaying similar documents to “A note on Schrödinger operators with polynomial potentials”

On operators satisfying the Rockland condition

Waldemar Hebisch (1998)

Studia Mathematica

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Let G be a homogeneous Lie group. We prove that for every closed, homogeneous subset Γ of G* which is invariant under the coadjoint action, there exists a regular kernel P such that P goes to 0 in any representation from Γ and P satisfies the Rockland condition outside Γ. We prove a subelliptic estimate as an application.

An inversion problem for singular integral operators on homogeneous groups

Paweł Głowacki (1987)

Studia Mathematica

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Hardy spaces associated with some Schrödinger operators

Jacek Dziubański, Jacek Zienkiewicz (1997)

Studia Mathematica

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For a Schrödinger operator A = -Δ + V, where V is a nonnegative polynomial, we define a Hardy $H_{A}^{1}$ space associated with A. An atomic characterization of $H_{A}^{1}$ is shown.

The Rockland condition for nondifferential convolution operators II

Paweł Głowacki (1991)

Studia Mathematica

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Asymptotics of sums of subcoercive operators

Nick Dungey, A. ter Elst, Derek Robinson (1999)

Colloquium Mathematicae

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We examine the asymptotic, or large-time, behaviour of the semigroup kernel associated with a finite sum of homogeneous subcoercive operators acting on a connected Lie group of polynomial growth. If the group is nilpotent we prove that the kernel is bounded by a convolution of two Gaussians whose orders correspond to the highest and lowest orders of the homogeneous subcoercive components of the generator. Moreover we establish precise asymptotic estimates on the difference of the kernel...

A functional calculus for Rockland operators on nilpotent Lie groups

Andrzej Hulanicki (1984)

Studia Mathematica

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On the eigenvalue asymptotics of certain Schrödinger operators

Wiesław Cupała (1993)

Studia Mathematica

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Subelliptic estimates on nilpotent Lie groups and the Cwikel-Lieb-Rosenblum inequality are used to estimate the number of eigenvalues for Schrödinger operators with polynomial potentials.

Nilpotent Lie groups and summability of eigenfunction expansions of Schrödinger operators

Andrzej Hulanicki, Joe Jenkins (1984)

Studia Mathematica

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Riesz means for the eigenfunction expansions for a class of hypo-elliptic differential operators

Giancarlo Mauceri (1981)

Annales de l'institut Fourier

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We study the Riesz means for the eigenfunction expansions of a class of hypoelliptic differential operators on the Heisenberg group. The operators we consider are homogeneous with respect to dilations and invariant under the action of the unitary group. We obtain convergence results in $L^{p}$ norm, at Lebesgue points and almost everywhere. We also prove localization results.

Note on semigroups generated by positive Rockland operators on graded homogeneous groups

Jacek Dziubański, Waldemar Hebisch, Jacek Zienkiewicz (1994)

Studia Mathematica

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Let L be a positive Rockland operator of homogeneous degree d on a graded homogeneous group G and let $p_{t}$ be the convolution kernels of the semigroup generated by L. We prove that if τ(x) is a Riemannian distance of x from the unit element, then there are constants c>0 and C such that $| p_{1} (x) | \leq C e x p (- c τ {(x)}^{d / (d - 1)})$ . Moreover, if G is not stratified, more precise estimates of $p_{1}$ at infinity are given.