Publications

Dissertation / PhD-thesis
U. FREIBERG: Maßgeometrische Laplaceoperatoren für fraktale Teilmengen der reellen Achse. Dissertation/PhD-thesis, Friedrich-Schiller-Universität Jena, 2000   ps  (german!)
 

Articles
(01) U. FREIBERG,  M. ZÄHLE: Harmonic Calculus on Fractals - A measure geometric approach I.  Potential Anal. 16 (2002), 265-277
(02) U. FREIBERG: A survey on measure geometric Laplacians on Cantor like sets. AJSE  28, No. 1C (2003), 189-198
(03) U. FREIBERG: Analytic properties of measure geometric Krein-Feller operators on the real line. Math. Nach. 260 (2003), 34-47
(04) U. FREIBERG,  J.-U. LÖBUS: Zeros of eigenfunctions of a class of generalized second order differential operators on the Cantor set.  Math. Nach. 265 (2004), 3-14   
(05) U. FREIBERG,  M. R. LANCIA: Energy form on a closed fractal curve. ZAA/1713 23 (2004) 1, 115-137 
(06) U. FREIBERG,  J.-U. LÖBUS: On the zeros of eigenfunctions of the generator of a gap diffusion. in: S. Albeverio, Z.-M. Ma, M. Röckner (eds.) Recent Developments in Stochastic Analysis and related topics, Proceedings of the First Sino-german meeting on stochastic analysis - satellite conference of the ICM, Bejing, PR China, 2002, World Scientific (2004), 182-198
(07) U. FREIBERG: Spectral asymptotics of generalized measure geometric Laplacians on Cantor like sets. Forum Math. 17 (2005), 87-104
(08) U. FREIBERG: Dirichlet forms on fractal subsets of the real line. Real Analysis Exchange 30 (2) (2004/2005), 589-604
(09) U. R. FREIBERG,  M. R. LANCIA: Energy forms on non self-similar fractals. in: C. Bandle, H. Berestycki (eds.) Elliptic and Parabolic Problems. A special Tribute to the Work of Haim Brezis. Series: Progress in Nonlinear Differential Equations and Their Applications, Vol. 63, Birkhäuser, Basel (2005), 267-277
(10) U. FREIBERG: Analysis on Fractal Objects. Meccanica 40 (2005), 419-436
(11) M. F. BARNSLEY, U. FREIBERG: Fractal transformations of harmonic functions. Proc. SPIE Vol. 6417, 64170C, Complexity and Nonlinear Dynamics; Axel Bender; Ed. (2007)
(12) U. FREIBERG,  M. R. LANCIA: Energy forms on conformal C¹-diffeomorphic images of the Sierpinski gasket. Math. Nach. 281 (2008), 337-349
(13) U. FREIBERG: Prüfer angle methods in spectral analysis of Krein-Feller operators. RIMS Kôkyuroku Bessatsu B6 (2008), 71-84

 

Preprints
U. FREIBERG,  M. R. LANCIA: Transmission problem on a closed fractal curve.
 

accepted



under review
U. FREIBERG: Einstein relation on fractals.
U. FREIBERG: On the interaction of geometry, analysis and stochastics on a body.
M. BARNSLEY, U. FREIBERG, and D. LA TORRE: Optimization on fractals objects and stability.
U. FREIBERG, D. LA TORRE, and F. MENDIVIL: Iterated function systems and stability of variational problems with multifunctions.

 

in preparation
U. FREIBERG: Random self similar sets in quasimetric spaces.
U. FREIBERG: Self conformal sets in quasimetric spaces.
U. FREIBERG,  M. LLORENTE: Minkowski measurability of self conformal sets.
U. FREIBERG,  M. R. LANCIA: Spectral asymptotics of fractal Laplace-Beltrami operators.
U. FREIBERG: A refinement of the spectral asymptotics of generalized measure geometric Laplacians on Cantor like sets.
U. FREIBERG: Gap diffusions on random Cantor sets.
U. FREIBERG: SDE driven by gap diffusions.

 

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