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.

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Zeitschriftenaufsatz | Veröffentlicht | Englisch
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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.
Erscheinungsjahr
Zeitschriftentitel
Infinite Dimensional Analysis, Quantum Probability and Related Topics
Band
5
Ausgabe
3
Seite(n)
297-315
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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. doi:10.1142/S0219025702000894
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.