Intrinsic ultracontractivity of the Feynman-Kac semigroup for relativistic stable processes
In: Transactions of the American Mathematical Society, Jg. 358 (2006), Heft 11, S. 5027-5057
Online
academicJournal
- print, 29 ref
Zugriff:
Let Xt be the relativistic α-stable process in Rd, a ∈ (0, 2), d > α, with infinitesimal generator H(α)0 = -((-A + m2/α)α/2 - m). We study intrinsic ultracontractivity (IU) for the Feynman-Kac semigroup Tt for this process with generator H(α)0 - V, V > 0, V locally bounded. We prove that if lim|x|→∞ V(x) = ∞, then for every t > 0 the operator Tt is compact. We consider the class V of potentials V such that V > 0, lim|x|→∞ V(x) = ∞ and V is comparable to the function which is radial, radially nondecreasing and comparable on unit balls. For V in the class V we show that the semigroup Tt is IU if and only if lim|x|→∞ V(x)/|x| = ∞. If this condition is satisfied we also obtain sharp estimates of the first eigenfunction Φ1 for Tt. In particular, when V(x) = |x|β, β > 0, then the semigroup Tt is IU if and only if β > 1. For β > 1 the first eigenfunction Φ1 (x) is comparable to.
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Intrinsic ultracontractivity of the Feynman-Kac semigroup for relativistic stable processes
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Autor/in / Beteiligte Person: | KULCZYCKI, Tadeusz ; SIUDEJA, Bartlomiej |
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Zeitschrift: | Transactions of the American Mathematical Society, Jg. 358 (2006), Heft 11, S. 5027-5057 |
Veröffentlichung: | Providence, RI: American Mathematical Society, 2006 |
Medientyp: | academicJournal |
Umfang: | print, 29 ref |
ISSN: | 0002-9947 (print) |
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