Subordination in the sense of S. Bochner - An approach through pseudo differential operators

Mathematische Nachrichten

Volumn 178, Issue , 1996, Pages 199-231

  Jacob, Niels ^a   Schilling, René L ^b  

^a TECHNICAL UNIVERSITY OF MUNICH   (Germany)

^b UNIVERSITY OF ERLANGEN NUREMBERG   (Germany)

Author keywords

Markov semigroups; Pseudo differential operators; Subordination

Indexed keywords

EID: 0013109786     PISSN: 0025584X     EISSN: None     Source Type: Journal    
DOI: 10.1002/mana.19961780110     Document Type: Article

References (28)

1. BERG, CHR., BOYADZHIEV, KH., and DE LAUBENFELS, R.: Generation of Generators of Holomorphic Semigroups, J. Austral. Math. Soc. (Ser. A) 55 (1993), 246-269
2. BERG, C., and FORST, G.: Potential Theory on Locally Compact Abelian Groups, Springer, Ergebnisse der Mathematik und ihrer Grenzgebiete, II. Ser. Vol. 87, Berlin 1975
3. BOCHNER, S.: Harmonic Analysis and the Theory of Probability, University of California Press, California Monographs in Math. Sci., Berkeley, CA 1955
4. BOULEAU, N.: Quelques Résultats Probabilistes sur la Subordination au Sens de Bochner. In: HIRSCH, F. et G. MOKOBODZKI (eds.): Séminaire de Théorie du Potentiel, Springer, Lecture Notes Math. Vol. 1061, Berlin 1984, 54-81
5. BOULEAU, N., et HIRSCH, F.: Formes de Dirichlet Générales et Densité des Variables Aléatoires Reelles sur l'Espace de Wiener, J. Func. Anal. 69 (1986), 229-259
6. DAVIES, E. B.: One-Parameter Semigroups, Academic Press, L. M. S. Monographs vol. 15, London 1980
7. DELLACHERIE, C., et MEYER, P.-A.: Probabilités et Potentiel: Chapitres XII à XVI, Hermann, Publications de l'Institut de Mathématique de l'Université de Strasbourg t. XIX, Paris 1987
8. FELLER, W.: An Introduction to Probability Theory and its Applications, Vol. 2, Wiley, Series in Prob. and Math. Stat., New York 1970 (2nd ed.)
9. FUKUSHIMA, M.: Dirichlet Forms and Markov Processes, North-Holland, Mathematical Library Vol. 23, Amsterdam 1980.
10. GRADSHTEYN, I., and RYZHIK, I.: Tables of Integrals, Series, and Products. Corrected and Enlarged Edition, Academic Press, San Diego, CA 1992 (7th ed.)
11. GRUBB, G.: Functional Calculus of Pseudo-Differential Boundary Problems, Birkhäuser, Progress in Math. Vol. 65, Boston 1986
12. GRUBB, G.: Parabolic Pseudo - Differential Boundary Problems and Applications. In: CATTABRIGA, L. and L. RODINO (eds.), Microlocal Analysis and Applications. Montecatini, Terme 1989, Springer, Lecture Notes Math. Vol. 1495, Berlin 1991, 46-117
13. GRUSCHIN, V. V.: Pseudodifferential Operators, Moscow Institute of Electrical Machines, Moskow 1975 (Russian)
14. HEINZ, E.: Beiträge zur Störungstheorie der Spektralzerlegung, Math. Ann. 123 (1951), 415-438
15. HIRSCH, F.: Intégrales de Résolvantes et Calcul Symbolique, Ann. Inst. Fourier 22 (1972), 239-264
16. HIRSCH, F.: Générateurs Etendus et Subordination au Sens de Bochner. In: HIRSCH, F. et G. MOKOBODZKI (eds.), Séminaire de Théorie du Potentiel, Springer, Lecture Notes Math. Vol. 1061, Berlin 1984, 134-156
17. HOH, W.: Pseudo Differential Operators with Negative Definite Symbols and the Martingale Problem, Stoch. and Stoch. Rep. (in press)
18. JACOB, N.: Further Pseudodifferential Operators Generating Feller Semigroups and Dirichlet Forms, Rev. Mat. Iberoam. 9 (1993), 373-407
19. JACOB, N.: A class of Feller semigroups generated by pseudo differential operators, Math. Z. 215 (1994), 151-166
20. JACOB, N.: Non-local (semi-) Dirichlet Forms Generated by Pseudo Differential Operators, in: MA, Z. M., RÖCKNER, M. and J. A. YAN (eds.), Dirichlet Forms and Stochastic Processes. Proc. Intnl. Conf. Dirichlet Forms and Stochastic Processes, p. 223-233, Beijing 1993, de Gruyter, Berlin 1995
21. JACOB, N., and LEOPOLD, H.-G.: Pseudo Differential Operators with Variable Order of Differentiation Generating Feller Semigroups, Integr. Equat. Oper. Th. 17 (1993), 544-553
22. LÖWNER, K.: Über monotone Matrixfunktionen, Math. Z. 38 (1934), 177-216
23. PAZY, A.: Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer, Applied Math. Ser. Vol. 44, Berlin 1983
24. PHILLIPS, R. S.: On the Generation of Semigroups of Linear Operators, Pac. J. Math. 2 (1952), 343-369
25. SCHILLING, R. L.: Zum Pfadverhalten von Markovschen Prozessen, die mit Lévy - Prozessen vergleichbar sind, Dissertation, Erlangen 1994
26. SCHILLING, R. L.: On the Domain of the Generator of a Subordinate Semigroup, to appear in: Proc. Intnl. Conf. Potential Theory, Kouty (CR) 1994, de Gruyter, Berlin 1996
27. SEELEY, R. Complex Powers of an Elliptic Operator. In: Singular Integrals Amer. Math. Soc., Proc. Symp. in Pure Math. Vol. 10, Providence, RI 1967
28. STRICHARTZ, R. S.: A Functional Calculus for Elliptic Pseudo-Differential Operators, Amer. Math. J. 94 (1972), 711-722