Generators of mehler-type semigroups as pseudo-differential operators
Lescot P, Röckner M (2002)
Infinite Dimensional Analysis, Quantum Probability and Related Topics 5(3): 297-315.
Zeitschriftenaufsatz
| Veröffentlicht | Englisch
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Autor*in
Lescot, Paul;
Röckner, MichaelUniBi
Einrichtung
Abstract / Bemerkung
We study semigroups (P-t)(tgreater than or equal to0) on a Hilbert space E, given by a Mehler-type formula: P(t)f(x) = integral(E)f(T(t)x + y)mut(dy). Under reasonable assumptions, the LP(E,mu)-generator A(0) of (P-t)(tgreater than or equal to0) turns out to be expressible as a pseudo-differential operator, provided p is an invariant measure for (P-t)(tgreater than or equal to0). The question of L-p-uniqueness is also answered positively.
Stichworte
pseudo-differential operators in infinite dimensions;
LP-uniqueness;
Mehler semigroup
Erscheinungsjahr
2002
Zeitschriftentitel
Infinite Dimensional Analysis, Quantum Probability and Related Topics
Band
5
Ausgabe
3
Seite(n)
297-315
ISSN
0219-0257
Page URI
https://pub.uni-bielefeld.de/record/1613297
Zitieren
Lescot P, Röckner M. Generators of mehler-type semigroups as pseudo-differential operators. Infinite Dimensional Analysis, Quantum Probability and Related Topics. 2002;5(3):297-315.
Lescot, P., & Röckner, M. (2002). Generators of mehler-type semigroups as pseudo-differential operators. Infinite Dimensional Analysis, Quantum Probability and Related Topics, 5(3), 297-315. https://doi.org/10.1142/S0219025702000894
Lescot, Paul, and Röckner, Michael. 2002. “Generators of mehler-type semigroups as pseudo-differential operators”. Infinite Dimensional Analysis, Quantum Probability and Related Topics 5 (3): 297-315.
Lescot, P., and Röckner, M. (2002). Generators of mehler-type semigroups as pseudo-differential operators. Infinite Dimensional Analysis, Quantum Probability and Related Topics 5, 297-315.
Lescot, P., & Röckner, M., 2002. Generators of mehler-type semigroups as pseudo-differential operators. Infinite Dimensional Analysis, Quantum Probability and Related Topics, 5(3), p 297-315.
P. Lescot and M. Röckner, “Generators of mehler-type semigroups as pseudo-differential operators”, Infinite Dimensional Analysis, Quantum Probability and Related Topics, vol. 5, 2002, pp. 297-315.
Lescot, P., Röckner, M.: Generators of mehler-type semigroups as pseudo-differential operators. Infinite Dimensional Analysis, Quantum Probability and Related Topics. 5, 297-315 (2002).
Lescot, Paul, and Röckner, Michael. “Generators of mehler-type semigroups as pseudo-differential operators”. Infinite Dimensional Analysis, Quantum Probability and Related Topics 5.3 (2002): 297-315.
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