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Kenneth Falconer - Books, Papers, Preprints


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Books

The Geometry of Fractal Sets, Cambridge UP, 1985; paperback 1986.

Fractal Geometry - Mathematical Foundations and Applications , John Wiley, Third Edition, 2014, with Solutions Manual 3rd Ed.

Unsolved Problems in Geometry (with H.T. Croft and R.K. Guy), Springer-Verlag, 1991.

Techniques in Fractal Geometry, John Wiley, 1997.

Fractals - A Very Short Introduction, Oxford UP, 2013.


Some selected papers

The Hausdorff dimension of self-affine fractals, Math. Proc. Cambridge Philos. Soc., 103 (1988), 339-350.

The dimension of self-affine fractals II, Math. Proc. Cambridge Philos. Soc., 111 (1992), 169-179.

Bounded distortion and dimension for non-conformal repellers, Math. Proc. Cambridge Philos. Soc. 115 (1994) 315-334.

The multifractal spectrum of statistically self-similar measures, J. Theoretical Probability, 7 (1994) 681-702.

Probabilistic methods in fractal geometry, Proc. Conf. Fractal Geometry and Stochastics, Finsterbergen 1994, Progress in Probability, 37 (1995), 3-13.

(with P. Mattila) The packing dimension of projections and sections of measures, Math. Proc. Cambridge Philos. Soc., 119 (1996), 695-713.

(with T.C. O'Neil) Vector-valued multifractal measures, Proc. Royal. Soc. Ser. A: Math and Phys. Sci., 452 (1996), 1433-1457.

(with J.D. Howroyd) Packing dimensions of projections and dimension profiles, Math. Proc. Cambridge Philos. Soc., 121 (1997), 269-286.

(with B. Lammering) Fractal properties of generalized Sierpinski triangles, Fractals,6 (1998), 31-41.

(with M Järvenpää) Packing dimensions of sections of sets, Math. Proc. Cambridge Philos. Soc., 125(1999), 89-104.

Generalised dimensions of measures on self-affine sets, Nonlinearity, 12(1999), 877-891.

Semilinear PDEs on self-similar fractals, Commun. Math. Phys. 206(1999), 235-245.

A nonlinear Mercerian theorem, J. Math. Anal. App. 239(1999), 440-448.

Representation of families of sets by measures, multifractal analysis and Diophantine approximation, Math. Proc. Cambridge Philos. Soc. 128(2000), 111-121.

(with J. Lévy Véhel) Horizons of fractional Brownian surfaces, Proc. Roy. Soc. London, Ser. A. 456(2000), 2153--2177

(with M. Järvenpää and P. Mattila) Examples illustrating the instability of packing dimensions of sections, Real Analysis Exchange, 25 (2000), 629--640.

(with R.D. Mauldin) Fubini-type theorems for general measure constructions, Mathematika, 47 (2000), 251--265.

(with J. Hu) Nonlinear diffusion equations on unbounded fractal domains, J. Math. Anal. App., 256(2001), 606--624.

Tangent fields and the local structure of random fields, J. Theoret. Probab. 15 (2002), 731--750.

The local structure of random processes, J. London Math. Soc.67 (2003), 657--672.

One-sided multifractal analysis and points of non-differentiability of devil's staircases,  Math. Proc. Cambridge Philos. Soc. 136 (2004), 167-174.

Dimensions of intersections and distance sets for polyhedral norms; Real Analysis Exchange, 30(2005),719--726.

(with J. O'Connor) Symmetry and enumeration of self-similar fractals; Bull. London Math. Soc., 39 (2007), 272-282.

(with C. Fernández) Inference on fractal processes using multiresolution approximation; Biometrika, 94 (2007), 313-334. Preprint

(with Y. Demichel) The Hausdorff dimension of pulse-sum graphs; Math. Proc. Cambridge Philos. Soc., 143 (2007), 145-155. Preprint

(with J. Miao) Dimensions of self-affine fractals and multifractals generated by upper-triangular matrices; Fractals, 15 (2007), 289-299. Preprint

(with J. Miao) Exceptional sets for self-affine fractals; Math. Proc. Cambridge Philos. Soc., 145 (2008), 669-684. Preprint , Cambridge Journals Online

(with J. Lévy Véhel) Multifractional, multistable, and other processes with prescribed local form, J. Theor. Probab., 22 (2009), 375-401. arXiv, SpringerLink DOI: 10.1007/s10959-008-0147-9

(with R. Le Guével and J. Lévy Véhel) Localisable moving average stable and multistable processes, Stochastic Models, 25 (2009), 648-672. arXiv

(with A. Sloan) Continuity of subadditive pressure for self-affine sets, Real Analysis Exchange, 34 (2009), 413-428. Preprint

(with J. Miao) Random subsets of self-affine fractals, Mathematika, 56 (2010), 61-76. Preprint , Cambridge Journals Online

Generalised dimensions of measures on almost self-affine sets, Nonlinearity, 23 (2010), 1047-1069. arXiv , IOPScience link

(with A. Samuel) Dixmier traces and coarse multifractal analysis; Ergodic Theory Dynam. Systems, 31 (2011), 369-381, arXiv

(with J.M. Fraser) The horizon problem for prevalent surfaces, Math. Proc. Cambridge Philos. Soc., 151 (2011), 355-372 , arXiv

(with Lining Liu) Multistable processes and localisability, Stochastic Models 28 (2012), 503-526, arXiv

(with Jiaxin Hu and Yuhua Sun) Inhomogeneous parabolic equations on unbounded metric measure spaces, Proc. Roy. Soc. Edinburgh A Mathematics 142 (2012), 1003-1025 , arXiv

(with J.M. Fraser) The visible part of plane self-similar sets, Proc. American Math. Soc. 141 (2013), 269-278, arXiv

(with G.C. Boore) Attractors of directed graph IFSs that are not standard IFS attractors and their Hausdorff measure, Math. Proc. Cambridge Philos. Soc. 154 (2013), 325-349

(with Yimin Xiao) Generalized dimensions of images of measures under Gaussian processes, Adv. Math.252 (2014), 492-517, arXiv

(with Xiong Jin) Exact dimensionality and projections of random self-similar measures and sets, J. London Math. Soc. 90 (2014), 388-412, arXiv

A Holder-type inequality on a regular rooted tree, J. Math. Analysis Appl. 423 (2015), 913-923, arXiv

(with Xiong Jin) Dimension conservation for self-similar sets and fractal percolation, Int. Math. Res. Notices, 2015(24) (2015), 13260-13289, arXiv

Higher moments for random multiplicative measures, J. Fractal Geometry 2 (2015), 229-247, arXiv

(with J.M. Fraser and Xiong Jin) Sixty years of fractal projections, in Fractal Geometry and Stochastics V, Progress in Probability 70, pp.3-25, Birkhauser (2015), arXiv

From fractional Brownian motion to multifractional and multistable motion, in Benoit Mandelbrot - A Life in Many Dimensions, pp.239-256, World Scientific, 2015

(with Casey Donoven) Codimension formulae for the intersection of fractal subsets of Cantor spaces, Proc. Amer. Math. Soc 144 (2016), 651-663, arXiv

(with Pertti Mattila) Strong Marstrand theorems and dimensions of sets formed by subsets of hyperplanes, J. Fractal Geometry 3 (2016), 319-329, arXiv

(with Tom Kempton) The dimension of projections of self-affine sets and measures, Annales Academiae Scientiarum Fennicae - Mathematica 42 (2017), 473-486, arXiv

(with Tom Kempton) Planar self-affine sets with equal Hausdorff, box and affinity dimensions, Ergodic Theory and Dynamical Systems 38 (2018), 1289-1341, arXiv

(with J. Lévy Véhel) Self-stabilizing processes, Stochastic Models 34 (2018), 409-434, arXiv

(with J. Lévy Véhel) Self-stabilizing processes based on random signs, J. Theoret. Probab.(2018), arXiv

(with V. Beresnevich, S. Velani, and A. Zafeiropoulos) Marstrand's Theorem revisited: projecting sets of dimension zero, J. Math. Analysis Appl. 472 (2019), 1820-1845 arXiv

(with Xiong Jin) Exact dimensionality and projection properties of Gaussian multiplicative chaos measures, Trans. Amer. Math. Soc. 372 (2019), 2921-2957 arXiv


Preprints

A capacity approach to box and packing dimensions of projections and other images, arXiv

A capacity approach to box and packing dimensions of projections of sets and exceptional directions, to appear, J. Fractal Geometry. arXiv


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