Analytical properties of measure geometric Krein-Feller-operators on the real line

Mathematische Nachrichten

Volumn 260, Issue , 2003, Pages 34-47

  Freiberg, Uta ^a  

^a FRIEDRICH SCHILLER UNIVERSITY JENA   (Germany)

Author keywords

Green function; Measure geometric Krein Feller operator; Resolvent operator

Indexed keywords

EID: 0242510919     PISSN: 0025584X     EISSN: None     Source Type: Journal    
DOI: 10.1002/mana.200310102     Document Type: Article

References (23)

1. M. Denker and S. Koch, A Poisson formula for harmonic functions on the Sierpinski gasket, Forum Math. 12 (4), 435-448 (2000).
2. M. Denker and H. Sato, Sierpinski gasket as a Martin boundary I: Martin kernels, Potential Anal. 14 (3), 211-232 (2001).
3. U. Freiberg, Maßgeometrische Laplaceoperatoren für fraktale Teilmengen der reellen Achse, PhD thesis, University of Jena (2000).
4. U. Freiberg, Spectral asymptotics of generalized measure geometric Laplacians on Cantor like sets, to appear in Forum Math.
5. U. Freiberg and J.-U. Löbus, The asymptotic distribution of the zeros of the eigenfunctions of a class of generalized second order differential operators on the Cantor set, to appear in Math. Nachr.
6. U. Freiberg and M. Zähle, Harmonic calculus on fractals - A measure geometric approach I, Potential Analysis 16, 265-277 (2002).
7. T. Fujita, A fractional dimension, self similarity and a generalized diffusion operator, Taniguchi Symp. PMMP Katata, 83-90 (1985).
8. K. Itô and H. P. jr. McKean, Diffusion processes and their sample paths (Springer-Verlag, Berlin-Heidelberg-New York, 1965).
9. J. Kigami, Harmonic calculus on p.c.f. self-similar sets, Trans. Am. Math. Soc. 335, 721-755 (1993).
10. H. König, Eigenvalue distribution of compact operators (Birkhäuser, Basel-Boston-Stuttgart, 1986).
11. S. Kotani, On asymptotic behaviour of the spectra of a one-dimensional Hamiltonian with a certain random coefficient, Publ. Res. Inst. Math. Sci. 12, 447-492 (1976).
12. U. Küchler, Some asymptotic properties of the transition densities of one-dimensional quasidiffusions, Publ. RIMS (Kyoto Univ.) 16, pp. 245-268 (1980).
13. U. Küchler, On sojourn times, excursions and spectral measures connencted with quasidiffusions, J. Math. Kyoto Univ. 26 (3), 403-421 (1986).
14. T. Lindstrøm, Brownian Motion on Nested Fractals, Memoirs Amer. Math. Soc. 420 (1990).
15. J.-U. Löbus, Generalized second order differential operators, Math. Nachr. 152, 229-245 (1991).
16. J.-U. Löbus, Constructions and generators of one-dimensional quasidiffusions with applications to selfaffine diffusions and Brownian motion on the Cantor set, Stoch. Stoch. Rep. 42, 93-114 (1993).
17. V. Metz, Shorted operators: An application in potential theory, Linear Algebra Appl. 264, 439-455 (1997).
18. C. Sabot, Existence and uniqueness of diffusions of finitely ramified self-similar fractals, Ann. Sci. Ec. Norm. Super., IV, Ser. 30 (5), 605-673 (1997).
19. H. Triebel, Höhere Analysis, Deutscher Verlag der Wissenschaften (Berlin, 1972).
20. H. Triebel, Fractals and Spectra related to Fourier Analysis and Function Spaces, Monographs in Mathematics 91 (Birkhäuser, Basel, 1997).
21. W. Walter, Gewöhnliche Differentialgleichungen, 6., überarb. u. erw. Aufl. (Springer-Verlag, Berlin-Heidelberg-New York, 1996).
22. D. Werner, Funktionalanalysis, 2., überarb. Aufl. (Springer-Verlag, Berlin-Heidelberg-New York, 1997).
23. K. Yosida, Functional Analysis, 6th ed. (Springer-Verlag, Berlin-Heidelberg-New York, 1980).