Publikationen

Recent publications and preprints

J. R ATAJ, M. ZÄHLE : Curvature densities of self-similar sets. Preprint.
S. WINTER, M. ZÄHLE : Fractal curvature measures of self-similar sets. Advances Geom. (to appear). (http://arxiv.org/abs/1007.0696)
M. HINZ, M. ZÄHLE : Semigroups, potential spaces and applications to (S)PDE. Potential Anal. (to appear). (PDF-file)
H. FINK, C. KLÜPPELBERG, M. ZÄHLE: Conditional characteristic functions of processes related to fractional Brownian motion. Preprint.
M. ZÄHLE : Lipschitz-Killing curvatures of self-similar random fractals. Trans. Amer. Math. Soc. 363 (2011), 2663-2684. (PDF-file)
J. HU, M. ZÄHLE: Schrödinger equations and heat kernel upper bounds on metric spaces. Forum Math. 22 (2010), 1213-1234.
M. HINZ, M. ZÄHLE : Gradient type noises II: Systems of partial differential equations. J. Funct. Anal. 256 (2009), 3192-3235. (PDF-file)
M. HINZ, M. ZÄHLE: Gradient type noises I: Partial and hybrid integrals. Complex Variables and Elliptic Equations 54 (2009), 561-583. (PDF-file)
J. HU, M. ZÄHLE: Generalized Bessel and Riesz potentials on metric measure spaces. Potential Anal. 30 (2009), 315-340.(PDF-file)
M. ZÄHLE: Potential spaces and traces of Lévy processes on h-sets. J. Contemp. Math. Anal. 44 (2009), 117-145 . (PDF-file) (http://www.springerlink.com/openurl.asp?genre=article&id=doi:10.3103/S1068362309020071)
V. KNOPOVA, M. ZÄHLE: Spaces of generalized smootness on h-sets and related Dirichlet forms. Studia Math. 174 (2006), 277-308. (PDF-file) (new version)
W. HANSEN, M. ZÄHLE: Restricting isotropic stable Lévy processes from R^n to fractal sets. Forum Math. 18 (2006), 171-191. (PDF-file)
J. RATAJ, M. ZÄHLE: General normal cycles and Lipschitz manifolds of bounded curvature. Annals Global Anal. Geom. 27 (2005), 135-156. (PDF-file)
J. HU, M. ZÄHLE: Potential spaces on fractals. Studia Math. 170 (2005), 259-281. (PDF-file)
J. HU, M. ZÄHLE: Jump processes and nonlinear fractional heat equations. Math. Nachr. 279 (2006), 1-14. (PS-file)
J. RATAJ, M. ZÄHLE: Normal cycles of Lipschitz manifolds by approximation with parallel sets. Diff. Geom. Appl. 19 (2003), 113-126. (PS-file)
M. ZÄHLE: Riesz potentials and Liouville operators on fractals. Potential Anal. 21 (2004), 193-208. (PDF-file)
M. ZÄHLE: Long range dependence, no arbitrage, and the Black--Scholes formula. Stochastics and Dynamics 2 (2002), 265-280. (PDF-file)
M. ZÄHLE: Riesz potentials and Besov spaces on fractals. In: Fractals in Graz 2001, Eds., Trends in Mathematics, Birkhäuser 2002, 271-276. ( PS -File)
M. ZÄHLE: Stochastic differential equations with fractal noise Math. Nachr. 278 (2005), 1097-1106. (PDF-file)
M. ZÄHLE: Harmonic calculus on fractals -- A measure--geometric approach II. Trans. Amer. Math. Soc. 357 (2005), 3407-3423. (PDF-file)

Publications 1996-2002

M. ZÄHLE, H. ZIEZOLD: Fractional derivatives of Weierstrass-type functions. J. Comput. Appl. Math. 76 (1996), 265-275.
M. ZÄHLE: Fractional differentiation in the self-affine case. V - The local degree of differentiability. Math. Nachr. 185 (1997), 279-306.
F. KLINGENHÖFER, M. ZÄHLE: Ordinary differential equations with fractal noise. Proc. Amer. Math. Soc. 127 (1999), 1021-1028.
M. ZÄHLE: Integration with respect to fractal functions and stochastic calculus I. Probab.Theory Relat. Fields 111 (1998), 333-374. (PDF-file)
M. ZÄHLE: Integration with respect to fractal functions and stochastic calculus II. Math. Nachr. 225 (2001), 145-183. (PDF-file)
M. ZÄHLE: On the link between fractional and stochastic calculus. in: Stochastic dynamics, (Eds. H. Crauel and M. Gundlach) Springer, New York 1999. (PS-file)
M. ZÄHLE: Non-osculating sets of positive reach. Geom. Dedicata 76 (1999), 183-187.
J. RATAJ, M. ZÄHLE: Curvatures and currents for unions of sets with positive reach II. Ann. Global Anal. Geom. 20 (2001), 1-21. (PS-file)
M. ZÄHLE: Local dimensions, average densities and self-conformal measures. Period. Math. Hung. 37 (1998), 217-225.
M. ZÄHLE: The average density of self-conformal measures. J. London Math. Soc. 63 (2001), 721-734.
U. FREIBERG, M. ZÄHLE: Harmonic calculus on fractals -- A measure--geometric approach I. Potential Anal. 16 (2002), 265-277.
M. ZÄHLE: Measure-theoretic Laplace operators on fractals. Canadian Math. Soc. Conference Proc. 29 (2000), 625-631.
M. ZÄHLE: Fractional integrals and derivatives with respect to a measure. Fract. Calculus Appl. Anal. 2 (1999), 537-542.
M. ZÄHLE: Forward integrals and stochastic differential equations In: Seminar on Stochastic Analysis, Random Fields and Applications III, Eds. R.C. Dalang, M. Dozzi, F. Russo, Progress in Probab., Birkhäuser 2002, 293-302. (PDF-file)
J. RATAJ, M. ZÄHLE: A remark on mixed curvature measures for sets with positive reach. Beiträge Algebra Geom.43 (2002), 171-179.
M. ZÄHLE: Riesz potentials of fractal measures. (Abstract). Real Anal. Exchange, 24th Summer Symp. Conf. Rep., May 2000, 109-110 .

Publications before 1996

The average fractal dimension and projections of measures and sets in R^n. Fractals 3 (1995), 747-754.
(with J. RATAJ) Mixed curvature measures for sets of positive reach and a translative integral formula. Geom. Dedicata 57 (1995), 259-283.
(with E. ARBEITER) Geometric measures for random mosaics in sperical spaces. Stoch. and Stoch. Reports 46 (1994), 63-77.
(with N. PATZSCHKE) Fractional differentiation in the self-affine case. IV--Random measures. Stoch. and Stoch. Reports 49 (1994), 87-98.
(with N. PATZSCHKE) Fractional differentiation in the self-affine case. III--The density of the Cantor set. Proc Amer. Math. Soc. 117 (1993),137-144.
(with N. PATZSCHKE) Fractional differentiation in the self-affine case. II--Extremal Processes. Stoch. Processes Appl. 45 (1993), 61-72.
(with N. PATZSCHKE) Fractional differentiation in the self-affine case. I-- Random functions. Stoch. Processes Appl. 43 (1992), 165-175.
(with N. PATZSCHKE) Self-similar measures are locally scale invariant. Probab. Theory Relat. Fields 97 (1993), 559-574.
(with L. LEISTRITZ) Topological mean value relations for random cell complexes. Math. Nachr. 155 (1992), 57-72.
(with E. ARBEITER) Kinematic relations for Hausdorff moment measures in sperical spaces. Math. Nachr. 153 (1991), 333-348.
Approximation and characterization of generalized Lipschitz-Killing curvatures. Ann. Global Anal. Geom. 8 (1990), 249-260.
Wicksell's corpuscle problem in sperical spaces. J. Appl.Prob. 27 (1990), 701-706.
A kinematic formula and moment measures of random sets. Math. Nachr. 149 (1990), 325-340.
(with W. ROTHER) Palm measures in homogeneous spaces. Math. Nachr. 149 (1990), 255-263.
(with W. ROTHER) A short proof of principal kinematic formula and extensions. Trans. Amer. Math. Soc. 321 (1990), 547-558.

Publications before 1990

Absolute curvature measures. Math. Nachr. 140 (1989), 83-90.
Random cell complexes and generalised sets. Ann. Probab. 16 (1988), 1742-1766.
(with V. WEISS) Geometric measures for random curved mosaics of R^d. Math. Nachr. 138 (1988), 313-326.
Normal cycles and second order rectifiable sets. (unpublished manuscript).
Polyhedron theorems for non-smooth cell complexes. Math. Nachr. 131 (1987), 299-310.
Curvatures and currents for unions of sets with positive reach. Geom. Dedicata 23 (1987), 155-171.
Integral and current representation of Federer's curvature measures. Arch. Math. 46 (1986), 557-567.
Curvature measures and random sets II. Probab. Th. Rel. Fields 71 (1986), 37-58.
Curvature measures and random sets I. Math. Nachr. 119 (1984), 327-339.
Thick section stereology for random fibres, Math. Operatiosforsch. Statist. 15 (1984), 429-435.
Random set processes in homogeneous Riemannian spaces. Math. Nachr. 110 (1983), 179-193.
Random processes of Hausdorff rectifiabble closed sets. Math. Nachr. 108 (1982), 49-72.
Ergodic properties of random fields and pattern with embedded point processes. Teor. Verojat. Primen. 27 (1982), 502-513.
Ergodic properties of general Palm measures. Math. Nachr. 95 (1980), 93-106.
On the Euler characteristic of excursions of random fields. Forschungserg. FSU, N/80/34 (1980)

Publications before 1980

On common invariance properties of translation invariant measures and their Palm measures. Forschungserg. FSU, N/79/44 (1979)
Ergodic theorems for Erlang pure loss systems in the case of dependent service times. Math. Nachr. 79 (1977), 317-323.