Edit Profile (opens in new tab) Falconer, Kenneth J. Co-Author Distance Author ID: falconer.kenneth-j Published as: Falconer, K. J.; Falconer, Kenneth; Falconer, Kenneth J.; Falconer, Kenneth T.; Falconer, K. more...less Homepage: http://www.mcs.st-andrews.ac.uk/~kenneth/ External Links: MGP · Wikidata · Google Scholar · dblp · GND · IdRef · theses.fr Documents Indexed: 145 Publications since 1976, including 9 Books 2 Contributions as Editor · 1 Further Contribution Co-Authors: 60 Co-Authors with 66 Joint Publications 1,356 Co-Co-Authors all top 5 Co-Authors 80 single-authored 9 Fraser, Jonathan MacDonald 5 Jin, Xiong 5 Lévy Véhel, Jacques 3 Barnsley, Michael Fielding 3 Croft, Hallard T. 3 Grimmett, Geoffrey R. 3 Hu, Jiaxin 3 Kempton, Tom 3 Marsh, D. T. 3 Mattila, Pertti 3 Miao, Jun 2 Bandt, Christoph 2 Burrell, Stuart A. 2 Frame, Michael Lee 2 Howroyd, John D. 2 Järvenpää, Maarit 2 Mumford, David Bryant 2 O’Neil, Toby C. 2 Stewart, Ian Nicholas 2 Xiao, Yimin 2 Yavicoli, Alexia 1 Barrallo, Javier 1 Beresnevich, Victor V. 1 Boore, G. C. 1 Brothers, Harlan J. 1 Cohen, Nathan 1 Coppens, Marc-Olivier 1 Demichel, Yann 1 Devaney, Robert L. 1 Donoven, Casey R. 1 Eglash, Ron 1 Fernández, Carmen 1 Fine, Benjamin L. 1 Furstenberg, Hillel 1 Guy, Richard Kenneth 1 Howe, Roger Evans 1 Jaffard, Stéphane 1 Käenmäki, Antti 1 Kahrobaei, Delaram 1 Kannan, V. 1 Kovač, Vjekoslav 1 Kumar, P. B. Vinod 1 Lammering, Birger 1 Le Guével, Ronan 1 Lee, Lawrence D. 1 Lesmoir-Gordon, Nigel 1 Liu, Lining 1 Marstrand, John M. 1 Mauldin, Richard Daniel 1 Meyer, Jens 1 O’Connor, John Joseph 1 Rogers, Claude Ambrose 1 Samuel, Tony 1 Shmerkin, Pablo S. 1 Sloan, Arron 1 Springer, O. B. 1 Sun, Yuhua 1 Troscheit, Sascha 1 Velani, Sanju L. 1 West, Bruce J. 1 Zafeiropoulos, Agamemnon 1 Zähle, Martina all top 5 Serials 24 Mathematical Proceedings of the Cambridge Philosophical Society 9 Mathematika 7 Journal of the London Mathematical Society. Second Series 7 Proceedings of the American Mathematical Society 7 Journal of Theoretical Probability 5 Journal of Mathematical Analysis and Applications 5 Bulletin of the London Mathematical Society 5 Journal of Fractal Geometry 3 Nonlinearity 3 Geometriae Dedicata 3 Real Analysis Exchange 3 Ergodic Theory and Dynamical Systems 3 Journal of Physics A: Mathematical and General 3 Stochastic Models 2 Communications in Mathematical Physics 2 Journal of Statistical Physics 2 Journal of Combinatorial Theory. Series A 2 Mathematische Zeitschrift 2 Proceedings of the London Mathematical Society. Third Series 2 Transactions of the American Mathematical Society 2 Notices of the American Mathematical Society 2 Fractals 1 American Mathematical Monthly 1 Journal d’Analyse Mathématique 1 Periodica Mathematica Hungarica 1 The Mathematical Intelligencer 1 Advances in Mathematics 1 Biometrika 1 Mathematische Nachrichten 1 Monatshefte für Mathematik 1 Statistics & Probability Letters 1 IMRN. International Mathematics Research Notices 1 Pokroky Matematiky, Fyziky & Astronomie 1 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 1 Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences 1 Stochastic Processes and their Applications 1 Annales Academiae Scientiarum Fennicae. Mathematica 1 Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 1 Cambridge Tracts in Mathematics 1 Progress in Probability 1 Groups, Complexity, Cryptology 1 Springer Proceedings in Mathematics & Statistics 1 Problem Books in Mathematics 1 Very Short Introductions 1 Cambridge Mathematical Library 1 London Mathematical Society. Newsletter all top 5 Fields 103 Measure and integration (28-XX) 38 Dynamical systems and ergodic theory (37-XX) 32 Probability theory and stochastic processes (60-XX) 15 Convex and discrete geometry (52-XX) 6 Number theory (11-XX) 6 Real functions (26-XX) 6 General topology (54-XX) 5 History and biography (01-XX) 5 Harmonic analysis on Euclidean spaces (42-XX) 5 Functional analysis (46-XX) 4 General and overarching topics; collections (00-XX) 4 Partial differential equations (35-XX) 3 Group theory and generalizations (20-XX) 3 Differential geometry (53-XX) 3 Statistical mechanics, structure of matter (82-XX) 2 Combinatorics (05-XX) 2 Potential theory (31-XX) 2 Sequences, series, summability (40-XX) 2 Operator theory (47-XX) 2 Geometry (51-XX) 2 Numerical analysis (65-XX) 2 Quantum theory (81-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Statistics (62-XX) 1 Operations research, mathematical programming (90-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 123 Publications have been cited 5,319 times in 3,889 Documents Cited by ▼ Year ▼ Fractal geometry: mathematical foundations and applications. Zbl 0689.28003Falconer, Kenneth 1,061 1990 The geometry of fractal sets. Zbl 0587.28004Falconer, K. J. 709 1985 Techniques in fractal geometry. Zbl 0869.28003Falconer, Kenneth 601 1997 Fractal geometry. Mathematical foundations and applications. 2nd ed. Zbl 1060.28005Falconer, Kenneth 532 2003 Fractal geometry. Mathematical foundations and applications. 3rd ed. Zbl 1285.28011Falconer, Kenneth 308 2014 Unsolved problems in geometry. Zbl 0748.52001Croft, Hallard T.; Falconer, Kenneth J.; Guy, Richard K. 198 1991 The Hausdorff dimension of self-affine fractals. Zbl 0642.28005Falconer, K. J. 158 1988 On the Hausdorff dimensions of distance sets. Zbl 0605.28005Falconer, K. J. 90 1985 Random fractals. Zbl 0623.60020Falconer, K. J. 86 1986 On the Lipschitz equivalence of Cantor sets. Zbl 0791.28006Falconer, K. J.; Marsh, D. T. 66 1992 The multifractal spectrum of statistically self-similar measures. Zbl 0805.60034Falconer, K. J. 63 1994 The dimension of self-affine fractals. II. Zbl 0797.28004Falconer, K. J. 48 1992 A subadditive thermodynamic formalism for mixing repellers. Zbl 0667.58029Falconer, K. J. 45 1988 Dimensions and measures of quasi self-semilinear sets. Zbl 0683.58034Falconer, K. J. 45 1989 Hausdorff measures. With a foreword by K. Falconer. Paperback ed. Zbl 0915.28002Rogers, C. A. 45 1998 The realization of small distances in plane sets of positive measure. Zbl 0599.28009Falconer, K. J. 44 1986 Sets with large intersection properties. Zbl 0798.28004Falconer, K. J. 43 1994 On the Minkowski measurability of fractals. Zbl 0838.28006Falconer, K. J. 42 1995 Packing dimensions of projections and dimension profiles. Zbl 0881.28002Falconer, K. J.; Howroyd, J. D. 42 1997 Fractal geometry: mathematical foundations and applications. Zbl 0871.28009Falconer, Kenneth 41 1997 Nonlinear elliptical equations on the Sierpiński gasket. Zbl 0942.35070Falconer, Kenneth J.; Hu, Jiaxin 38 1999 The local structure of random processes. Zbl 1054.28003Falconer, Kenneth J. 38 2003 Classification of quasi-circles by Hausdorff dimension. Zbl 0684.58023Falconer, K. J.; Marsh, D. T. 37 1989 Tangent fields and the local structure of random fields. Zbl 1013.60028Falconer, Kenneth J. 35 2002 Bounded distortion and dimension for non-conformal repellers. Zbl 0808.58028Falconer, K. J. 34 1994 Semilinear PDEs on self-similar fractals. Zbl 0940.35080Falconer, K. J. 31 1999 Dimensions of self-affine fractals and multifractals generated by upper-triangular matrices. Zbl 1137.28302Falconer, Kenneth; Miao, Jun 31 2007 Hausdorff dimension and the exceptional set of projections. Zbl 0477.28004Falconer, K. J. 29 1982 Exact dimensionality and projections of random self-similar measures and sets. Zbl 1305.28010Falconer, Kenneth J.; Jin, Xiong 28 2014 Generalized dimensions of measures on self-affine sets. Zbl 0946.28004Falconer, K. J. 27 1999 The realization of distances in measurable subsets covering \(R^ n\). Zbl 0469.05021Falconer, K. J. 26 1981 The packing dimension of projections and sections of measures. Zbl 0867.28005Falconer, Kenneth J.; Mattila, Pertti 26 1996 Sixty years of fractal projections. Zbl 1338.28007Falconer, Kenneth; Fraser, Jonathan; Jin, Xiong 26 2015 Multifractional, multistable, and other processes with Prescribed local form. Zbl 1171.60010Falconer, K. J.; Lévy Véhel, J. 25 2009 Projection theorems for box and packing dimensions. Zbl 0846.28004Falconer, K. J.; Howroyd, J. D. 25 1996 Planar self-affine sets with equal Hausdorff, box and affinity dimensions. Zbl 1388.37028Falconer, Kenneth; Kempton, Tom 22 2018 Convolutions and the geometry of multifractal measures. Zbl 1040.28011Falconer, K. J.; O’Neil, T. C. 21 1999 On the geometry of random Cantor sets and fractal percolation. Zbl 0752.60007Falconer, K. J.; Grimmett, G. R. 19 1992 Continuity of subadditive pressure for self-affine sets. Zbl 1196.37046Falconer, Kenneth; Sloan, Arron 19 2009 Plane sets with positive density at infinity contain all large distances. Zbl 0599.28008Falconer, K. J.; Marstrand, J. M. 17 1986 The Hausdorff dimension of some fractals and attractors of overlapping construction. Zbl 0694.58028Falconer, K. J. 17 1987 The horizon problem for prevalent surfaces. Zbl 1235.28005Falconer, K. J.; Fraser, J. M. 17 2011 Classes of sets with large intersection. Zbl 0606.28003Falconer, K. J. 16 1985 Sub-self-similar sets. Zbl 0844.28005Falconer, K. J. 16 1995 Wavelet transforms and order-two densities of fractals. Zbl 0893.28006Falconer, K. J. 15 1992 Nonlinear diffusion equations on unbounded fractal domains. Zbl 0997.35026Falconer, Kenneth J.; Hu, Jiaxin 15 2001 Continuity properties of k-plane integrals and Besicovitch sets. Zbl 0438.42014Falconer, K. J. 15 1980 Localizable moving average symmetric stable and multistable processes. Zbl 1221.60049Falconer, Kenneth J.; Le Guével, Ronan; Lévy-Véhel, Jacques 15 2009 Generalized dimensions of measures on almost self-affine sets. Zbl 1196.28015Falconer, Kenneth J. 14 2010 The visible part of plane self-similar sets. Zbl 1267.28006Falconer, Kenneth J.; Fraser, Jonathan M. 14 2013 Intermediate dimensions. Zbl 1448.28009Falconer, Kenneth J.; Fraser, Jonathan M.; Kempton, Tom 14 2020 Applications of a result on spherical integration to the theory of convex sets. Zbl 0529.52001Falconer, K. J. 13 1983 The dimension of the convex kernel of a compact starshaped set. Zbl 0374.52006Falconer, K. J. 13 1977 Dimensions of self-affine sets: a survey. Zbl 1268.28013Falconer, Kenneth 13 2013 One-sided multifractal analysis and points of non-differentiability of devil’s staircases. Zbl 1046.28005Falconer, Kenneth J. 13 2004 Projection theorems for intermediate dimensions. Zbl 1470.28007Burrell, Stuart A.; Falconer, Kenneth J.; Fraser, Jonathan M. 13 2021 Multistable processes and localizability. Zbl 1270.60047Falconer, Kenneth; Liu, Lining 12 2012 Sets with prescribed projections and Nikodým sets. Zbl 0602.28005Falconer, K. J. 11 1986 X-ray problems for point sources. Zbl 0481.52002Falconer, K. J. 11 1983 Dimension conservation for self-similar sets and fractal percolation. Zbl 1351.28012Falconer, Kenneth; Jin, Xiong 11 2015 Cut-set sums and tree processes. Zbl 0636.90031Falconer, K. J. 10 1987 On a problem of Erdős on fractal combinatorial geometry. Zbl 0749.52013Falconer, K. J. 10 1992 On a problem of Erdoes on sequences and measurable sets. Zbl 0528.28005Falconer, K. J. 10 1984 Projections of random Cantor sets. Zbl 0681.60016Falconer, K. J. 10 1989 Representation of families of sets by measures, dimension spectra and Diophantine approximation. Zbl 0962.28003Falconer, K. J. 9 2000 Symmetry and enumeration of self-similar fractals. Zbl 1148.28006Falconer, Kenneth J.; O’Connor, John J. 9 2007 Strong Marstrand theorems and dimensions of sets formed by subsets of hyperplanes. Zbl 1365.28003Falconer, Kenneth; Mattila, Pertti 9 2016 The dimension of projections of self-affine sets and measures. Zbl 1365.28006Falconer, Kenneth; Kempton, Tom 9 2017 Random subsets of self-affine fractals. Zbl 1185.28013Falconer, Kenneth; Miao, Jun 9 2010 Exceptional sets for self-affine fractals. Zbl 1158.28002Falconer, Kenneth; Miao, Jun 9 2008 Dixmier traces and coarse multifractal analysis. Zbl 1236.28006Falconer, Kenneth; Samuel, Tony 7 2011 A capacity approach to box and packing dimensions of projections and other images. Zbl 1454.28008Falconer, K. J. 7 2020 A result on the Steiner symmetrization of a compact set. Zbl 0343.52002Falconer, K. J. 6 1976 Hammer’s X-ray problem and the stable manifold theorem. Zbl 0494.52002Falconer, K. J. 6 1983 Vector-valued multifractal measures. Zbl 0878.28005Falconer, Kenneth J.; O’Neil, Toby C. 6 1996 A capacity approach to box and packing dimensions of projections of sets and exceptional directions. Zbl 1473.28007Falconer, Kenneth J. 6 2021 On the equireciprocal point problem. Zbl 0523.52004Falconer, K. J. 5 1983 Rings of fractional dimension. Zbl 0529.28007Falconer, K. J. 5 1984 The critical point of fractal percolation in three and more dimensions. Zbl 0728.60102Falconer, K. J.; Grimmett, G. R. 5 1991 Attractors of directed graph IFSs that are not standard IFS attractors and their Hausdorff measure. Zbl 1290.37025Boore, G. C.; Falconer, K. J. 5 2013 Minkowski dimension for measures. Zbl 07630928Falconer, Kenneth J.; Fraser, Jonathan M.; Käenmäki, Antti 5 2023 Intermediate dimensions: a survey. Zbl 1484.28007Falconer, Kenneth J. 5 2021 The integral geometry of fractals. Zbl 0687.28004Falconer, K. J. 4 1989 Growth rate of an endomorphism of a group. Zbl 1243.20053Falconer, Kenneth J.; Fine, Benjamin; Kahrobaei, Delaram 4 2011 Inhomogeneous parabolic equations on unbounded metric measure spaces. Zbl 1258.35124Falconer, Kenneth J.; Hu, Jiaxin; Sun, Yuhua 4 2012 Probabilistic methods in fractal geometry. Zbl 0839.28003Falconer, Kenneth J. 4 1995 \(L^q\)-spectra of measures on planar non-conformal attractors. Zbl 1482.28010Falconer, Kenneth J.; Fraser, Jonathan M.; Lee, Lawrence D. 4 2021 Consistency conditions for a finite set of projections of a function. Zbl 0386.28008Falconer, K. J. 4 1979 Packing dimensions of sections of sets. Zbl 0922.28005Falconer, K. J.; Järvenpää, M. 4 1999 Correction: On the geometry of random Cantor sets and fractal percolation. Zbl 0786.60014Falconer, K. J.; Grimmett, G. R. 4 1994 The Hausdorff dimension of pulse-sum graphs. Zbl 1123.60023Demichel, Yann; Falconer, Kenneth 4 2007 Fractal properties of generalized Sierpiński triangles. Zbl 1012.28012Falconer, Kenneth J.; Lammering, Birger 4 1998 Inference on fractal processes using multiresolution approximation. Zbl 1133.62068Falconer, Kenneth; Fernández, Carmen 4 2007 Generalized dimensions of images of measures under Gaussian processes. Zbl 1292.60047Falconer, Kenneth; Xiao, Yimin 4 2014 Digital sundials, paradoxical sets, and Vitushkin’s conjecture. Zbl 0609.28005Falconer, K. J. 3 1987 Marstrand’s theorem revisited: projecting sets of dimension zero. Zbl 1411.28003Beresnevich, Victor; Falconer, Kenneth; Velani, Sanju; Zafeiropoulos, Agamemnon 3 2019 Intermediate dimension of images of sequences under fractional Brownian motion. Zbl 1478.60124Falconer, Kenneth J. 3 2022 The fractal structure of elliptical polynomial spirals. Zbl 1510.28006Burrell, S. A.; Falconer, K. J.; Fraser, J. M. 3 2022 Examples illustrating the instability of packing dimensions of sections. Zbl 1016.28006Falconer, K. J.; Järvenpää, M.; Mattila, P. 3 2000 Sections of sets of zero Lebesgue measure. Zbl 0426.28006Falconer, K. J. 3 1980 Minkowski dimension for measures. Zbl 07630928Falconer, Kenneth J.; Fraser, Jonathan M.; Käenmäki, Antti 5 2023 Intermediate dimension of images of sequences under fractional Brownian motion. Zbl 1478.60124Falconer, Kenneth J. 3 2022 The fractal structure of elliptical polynomial spirals. Zbl 1510.28006Burrell, S. A.; Falconer, K. J.; Fraser, J. M. 3 2022 Intersections of thick compact sets in \(\mathbb{R}^d\). Zbl 1514.11017Falconer, Kenneth; Yavicoli, Alexia 2 2022 Projection theorems for intermediate dimensions. Zbl 1470.28007Burrell, Stuart A.; Falconer, Kenneth J.; Fraser, Jonathan M. 13 2021 A capacity approach to box and packing dimensions of projections of sets and exceptional directions. Zbl 1473.28007Falconer, Kenneth J. 6 2021 Intermediate dimensions: a survey. Zbl 1484.28007Falconer, Kenneth J. 5 2021 \(L^q\)-spectra of measures on planar non-conformal attractors. Zbl 1482.28010Falconer, Kenneth J.; Fraser, Jonathan M.; Lee, Lawrence D. 4 2021 Assouad dimension influences the box and packing dimensions of orthogonal projections. Zbl 1493.28012Falconer, Kenneth J.; Fraser, Jonathan M.; Shmerkin, Pablo 2 2021 Intermediate dimensions. Zbl 1448.28009Falconer, Kenneth J.; Fraser, Jonathan M.; Kempton, Tom 14 2020 A capacity approach to box and packing dimensions of projections and other images. Zbl 1454.28008Falconer, K. J. 7 2020 Self-stabilizing processes based on random signs. Zbl 1457.60057Falconer, K. J.; Lévy Véhel, J. 2 2020 Marstrand’s theorem revisited: projecting sets of dimension zero. Zbl 1411.28003Beresnevich, Victor; Falconer, Kenneth; Velani, Sanju; Zafeiropoulos, Agamemnon 3 2019 Planar self-affine sets with equal Hausdorff, box and affinity dimensions. Zbl 1388.37028Falconer, Kenneth; Kempton, Tom 22 2018 Self-stabilizing processes. Zbl 1411.60057Falconer, K. J.; Lévy Véhel, J. 2 2018 The dimension of projections of self-affine sets and measures. Zbl 1365.28006Falconer, Kenneth; Kempton, Tom 9 2017 Strong Marstrand theorems and dimensions of sets formed by subsets of hyperplanes. Zbl 1365.28003Falconer, Kenneth; Mattila, Pertti 9 2016 Codimension formulae for the intersection of fractal subsets of Cantor spaces. Zbl 1334.28016Donoven, Casey; Falconer, Kenneth 1 2016 Sixty years of fractal projections. Zbl 1338.28007Falconer, Kenneth; Fraser, Jonathan; Jin, Xiong 26 2015 Dimension conservation for self-similar sets and fractal percolation. Zbl 1351.28012Falconer, Kenneth; Jin, Xiong 11 2015 A Hölder-type inequality on a regular rooted tree. Zbl 1302.05033Falconer, K. J. 2 2015 From fractional Brownian motion to multifractional and multistable motion. Zbl 1330.60060Falconer, Kenneth 1 2015 Fractal geometry. Mathematical foundations and applications. 3rd ed. Zbl 1285.28011Falconer, Kenneth 308 2014 Exact dimensionality and projections of random self-similar measures and sets. Zbl 1305.28010Falconer, Kenneth J.; Jin, Xiong 28 2014 Generalized dimensions of images of measures under Gaussian processes. Zbl 1292.60047Falconer, Kenneth; Xiao, Yimin 4 2014 The visible part of plane self-similar sets. Zbl 1267.28006Falconer, Kenneth J.; Fraser, Jonathan M. 14 2013 Dimensions of self-affine sets: a survey. Zbl 1268.28013Falconer, Kenneth 13 2013 Attractors of directed graph IFSs that are not standard IFS attractors and their Hausdorff measure. Zbl 1290.37025Boore, G. C.; Falconer, K. J. 5 2013 Fractals. A very short introduction. Zbl 1279.28001Falconer, Kenneth 2 2013 Multistable processes and localizability. Zbl 1270.60047Falconer, Kenneth; Liu, Lining 12 2012 Inhomogeneous parabolic equations on unbounded metric measure spaces. Zbl 1258.35124Falconer, Kenneth J.; Hu, Jiaxin; Sun, Yuhua 4 2012 Glimpses of Benoît B. Mandelbrot (1924–2010). Zbl 1284.01047Stewart, Ian; Mumford, David; Falconer, Kenneth; Eglash, Ron; Brothers, Harlan; Lesmoir-Gordon, Nigel; Barrallo, Javier; Berry, Michael; Frame, Michael 1 2012 The influence of Benoît B. Mandelbrot on mathematics. Zbl 1284.01048Stewart, Ian; Mumford, David; Howe, Roger; Furstenberg, Hillel; Falconer, Kenneth; West, Bruce J.; Coppens, Marc-Olivier; Cohen, Nathan; Jaffard, Stéphane; Berry, Michael; Frame, Michael 1 2012 The horizon problem for prevalent surfaces. Zbl 1235.28005Falconer, K. J.; Fraser, J. M. 17 2011 Dixmier traces and coarse multifractal analysis. Zbl 1236.28006Falconer, Kenneth; Samuel, Tony 7 2011 Growth rate of an endomorphism of a group. Zbl 1243.20053Falconer, Kenneth J.; Fine, Benjamin; Kahrobaei, Delaram 4 2011 Generalized dimensions of measures on almost self-affine sets. Zbl 1196.28015Falconer, Kenneth J. 14 2010 Random subsets of self-affine fractals. Zbl 1185.28013Falconer, Kenneth; Miao, Jun 9 2010 Multifractional, multistable, and other processes with Prescribed local form. Zbl 1171.60010Falconer, K. J.; Lévy Véhel, J. 25 2009 Continuity of subadditive pressure for self-affine sets. Zbl 1196.37046Falconer, Kenneth; Sloan, Arron 19 2009 Localizable moving average symmetric stable and multistable processes. Zbl 1221.60049Falconer, Kenneth J.; Le Guével, Ronan; Lévy-Véhel, Jacques 15 2009 Exceptional sets for self-affine fractals. Zbl 1158.28002Falconer, Kenneth; Miao, Jun 9 2008 Dimensions of self-affine fractals and multifractals generated by upper-triangular matrices. Zbl 1137.28302Falconer, Kenneth; Miao, Jun 31 2007 Symmetry and enumeration of self-similar fractals. Zbl 1148.28006Falconer, Kenneth J.; O’Connor, John J. 9 2007 The Hausdorff dimension of pulse-sum graphs. Zbl 1123.60023Demichel, Yann; Falconer, Kenneth 4 2007 Inference on fractal processes using multiresolution approximation. Zbl 1133.62068Falconer, Kenneth; Fernández, Carmen 4 2007 Dimensions of intersections and distance sets for polyhedral norms. Zbl 1107.28008Falconer, K. J. 3 2005 One-sided multifractal analysis and points of non-differentiability of devil’s staircases. Zbl 1046.28005Falconer, Kenneth J. 13 2004 Fractal geometry. Mathematical foundations and applications. 2nd ed. Zbl 1060.28005Falconer, Kenneth 532 2003 The local structure of random processes. Zbl 1054.28003Falconer, Kenneth J. 38 2003 Tangent fields and the local structure of random fields. Zbl 1013.60028Falconer, Kenneth J. 35 2002 Nonlinear diffusion equations on unbounded fractal domains. Zbl 0997.35026Falconer, Kenneth J.; Hu, Jiaxin 15 2001 Representation of families of sets by measures, dimension spectra and Diophantine approximation. Zbl 0962.28003Falconer, K. J. 9 2000 Examples illustrating the instability of packing dimensions of sections. Zbl 1016.28006Falconer, K. J.; Järvenpää, M.; Mattila, P. 3 2000 Fubini-type theorems for general measure constructions. Zbl 1010.28005Falconer, K. J.; Mauldin, R. Daniel 2 2000 Horizons of fractional Brownian surfaces. Zbl 0969.60083Falconer, K. J.; Lévy Véhel, J. 1 2000 Nonlinear elliptical equations on the Sierpiński gasket. Zbl 0942.35070Falconer, Kenneth J.; Hu, Jiaxin 38 1999 Semilinear PDEs on self-similar fractals. Zbl 0940.35080Falconer, K. J. 31 1999 Generalized dimensions of measures on self-affine sets. Zbl 0946.28004Falconer, K. J. 27 1999 Convolutions and the geometry of multifractal measures. Zbl 1040.28011Falconer, K. J.; O’Neil, T. C. 21 1999 Packing dimensions of sections of sets. Zbl 0922.28005Falconer, K. J.; Järvenpää, M. 4 1999 Hausdorff measures. With a foreword by K. Falconer. Paperback ed. Zbl 0915.28002Rogers, C. A. 45 1998 Fractal properties of generalized Sierpiński triangles. Zbl 1012.28012Falconer, Kenneth J.; Lammering, Birger 4 1998 Techniques in fractal geometry. Zbl 0869.28003Falconer, Kenneth 601 1997 Packing dimensions of projections and dimension profiles. Zbl 0881.28002Falconer, K. J.; Howroyd, J. D. 42 1997 Fractal geometry: mathematical foundations and applications. Zbl 0871.28009Falconer, Kenneth 41 1997 The packing dimension of projections and sections of measures. Zbl 0867.28005Falconer, Kenneth J.; Mattila, Pertti 26 1996 Projection theorems for box and packing dimensions. Zbl 0846.28004Falconer, K. J.; Howroyd, J. D. 25 1996 Vector-valued multifractal measures. Zbl 0878.28005Falconer, Kenneth J.; O’Neil, Toby C. 6 1996 On the Minkowski measurability of fractals. Zbl 0838.28006Falconer, K. J. 42 1995 Sub-self-similar sets. Zbl 0844.28005Falconer, K. J. 16 1995 Probabilistic methods in fractal geometry. Zbl 0839.28003Falconer, Kenneth J. 4 1995 Order-two density of sets and measures with non-integral dimension. Zbl 0848.28002Falconer, K. J.; Springer, O. B. 3 1995 Average densities of the image and zero set of stable processes. Zbl 0819.60038Falconer, K. J.; Xiao, Y. M. 2 1995 The multifractal spectrum of statistically self-similar measures. Zbl 0805.60034Falconer, K. J. 63 1994 Sets with large intersection properties. Zbl 0798.28004Falconer, K. J. 43 1994 Bounded distortion and dimension for non-conformal repellers. Zbl 0808.58028Falconer, K. J. 34 1994 Correction: On the geometry of random Cantor sets and fractal percolation. Zbl 0786.60014Falconer, K. J.; Grimmett, G. R. 4 1994 On the Lipschitz equivalence of Cantor sets. Zbl 0791.28006Falconer, K. J.; Marsh, D. T. 66 1992 The dimension of self-affine fractals. II. Zbl 0797.28004Falconer, K. J. 48 1992 On the geometry of random Cantor sets and fractal percolation. Zbl 0752.60007Falconer, K. J.; Grimmett, G. R. 19 1992 Wavelet transforms and order-two densities of fractals. Zbl 0893.28006Falconer, K. J. 15 1992 On a problem of Erdős on fractal combinatorial geometry. Zbl 0749.52013Falconer, K. J. 10 1992 Unsolved problems in geometry. Zbl 0748.52001Croft, Hallard T.; Falconer, Kenneth J.; Guy, Richard K. 198 1991 The critical point of fractal percolation in three and more dimensions. Zbl 0728.60102Falconer, K. J.; Grimmett, G. R. 5 1991 The horizon problem for random surfaces. Zbl 0718.60045Falconer, K. J. 2 1991 Dimensions - their determination and properties. Zbl 0734.28008Falconer, Kenneth J. 2 1991 Fractal geometry: mathematical foundations and applications. Zbl 0689.28003Falconer, Kenneth 1,061 1990 Dimensions and measures of quasi self-semilinear sets. Zbl 0683.58034Falconer, K. J. 45 1989 Classification of quasi-circles by Hausdorff dimension. Zbl 0684.58023Falconer, K. J.; Marsh, D. T. 37 1989 Projections of random Cantor sets. Zbl 0681.60016Falconer, K. J. 10 1989 The integral geometry of fractals. Zbl 0687.28004Falconer, K. J. 4 1989 The Hausdorff dimension of self-affine fractals. Zbl 0642.28005Falconer, K. J. 158 1988 A subadditive thermodynamic formalism for mixing repellers. Zbl 0667.58029Falconer, K. J. 45 1988 The dimension of affine-invariant fractals. Zbl 0651.58021Falconer, K. J.; Marsh, D. T. 1 1988 The Hausdorff dimension of some fractals and attractors of overlapping construction. Zbl 0694.58028Falconer, K. J. 17 1987 Cut-set sums and tree processes. Zbl 0636.90031Falconer, K. J. 10 1987 Digital sundials, paradoxical sets, and Vitushkin’s conjecture. Zbl 0609.28005Falconer, K. J. 3 1987 Random fractals. Zbl 0623.60020Falconer, K. J. 86 1986 The realization of small distances in plane sets of positive measure. Zbl 0599.28009Falconer, K. J. 44 1986 ...and 23 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 3,627 Authors 65 Falconer, Kenneth J. 53 Xi, Lifeng 50 Fraser, Jonathan MacDonald 38 Olsen, Lars Ole Ronnow 38 Wu, Min 33 Xiao, Yimin 30 Shmerkin, Pablo S. 29 Feng, De-Jun 27 Lau, Kasing 26 Iosevich, Alex 25 Simon, Károly 24 Li, Bing 24 Rams, Michał 23 Barral, Julien 23 Selmi, Bilel 22 Bárány, Balázs 22 Li, Wenxia 22 Peres, Yuval 22 Su, Weiyi 22 Wu, Jun 20 Käenmäki, Antti 20 Solomyak, Boris 20 Urbański, Mariusz 19 Li, Jinjun 19 Lutz, Jack H. 18 Bory Reyes, Juan 18 Kesseböhmer, Marc 18 Lapidus, Michel L. 18 Ngai, Sze-Man 18 Seuret, Stéphane 18 Xiong, Ying 17 Liang, Yongshun 17 Mattila, Pertti 17 Yu, Han 16 Fernández-Sánchez, Juan 16 He, Xinggang 16 Järvenpää, Maarit 16 Simmons, David 16 Suomala, Ville 16 Wen, Shengyou 15 Abreu-Blaya, Ricardo 15 Buczolich, Zoltán 15 Fernández Martínez, Manuel 15 Kong, Derong 15 Morris, Ian D. 15 Rao, Hui 15 Robinson, James Cooper 15 Ruan, Huo-Jun 14 Anh, Vo V. 14 De Amo, Enrique 14 Diaz Carrillo, Manuel 14 Hare, Kathryn E. 14 Järvenpää, Esa 14 Jiang, Kan 14 Lévy Véhel, Jacques 14 Pollicott, Mark 14 Staiger, Ludwig 14 Wen, Zhixiong 14 Zhou, Zuoling 13 Ayache, Antoine 13 Chen, Changhao 13 Dai, Meifeng 13 Dumitrescu, Adrian 13 Keleti, Tamás 13 Lancia, Maria Rosaria 13 Orponen, Tuomas 13 Sánchez Granero, Miguel Ángel 13 Troscheit, Sascha 13 Velani, Sanju L. 13 Wen, Zhi-Ying 13 Zhao, Yun 13 Zhu, Sanguo 12 Allaart, Pieter C. 12 Attia, Najmeddine 12 Balogh, Zoltán M. 12 Bandt, Christoph 12 Bugeaud, Yann 12 Golmankhaneh, Alireza Khalili 12 Mauldin, Richard Daniel 12 Neunhäuserer, Jörg 12 Priyadarshi, Amit 12 Roychowdhury, Mrinal Kanti 12 Winter, Steffen 12 Zähle, Martina 12 Žubrinić, Darko 11 Balankin, Alexander S. 11 Cao, Yongluo 11 Jaffard, Stéphane 11 Jin, Xiong 11 Mayordomo, Elvira 11 Panagiotopoulos, Panagiotis D. 11 Strichartz, Robert S. 11 Taylor, Krystal 11 Verma, Saurabh 11 Yao, Kui 10 Baker, Simon 10 Ben Slimane, Mourad 10 Fan, Ai Hua 10 Hu, Dihe 10 Hussain, Mumtaz ...and 3,527 more Authors all top 5 Cited in 549 Serials 215 Journal of Mathematical Analysis and Applications 171 Fractals 134 Chaos, Solitons and Fractals 133 Proceedings of the American Mathematical Society 118 Advances in Mathematics 109 Transactions of the American Mathematical Society 87 Ergodic Theory and Dynamical Systems 65 Monatshefte für Mathematik 61 Mathematical Proceedings of the Cambridge Philosophical Society 51 Journal of Fractal Geometry 50 Communications in Mathematical Physics 46 Journal of Statistical Physics 44 Israel Journal of Mathematics 43 Journal of Functional Analysis 43 Mathematische Zeitschrift 42 Nonlinearity 41 Stochastic Processes and their Applications 38 Mathematika 36 Mathematische Nachrichten 35 Journal d’Analyse Mathématique 35 Journal of Theoretical Probability 32 Topology and its Applications 28 Discrete Mathematics 28 Discrete & Computational Geometry 27 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 26 Applied Mathematics and Computation 26 Acta Mathematica Sinica. English Series 25 Journal of Number Theory 25 The Journal of Geometric Analysis 25 The Journal of Fourier Analysis and Applications 25 Analysis in Theory and Applications 24 Physica A 23 Statistics & Probability Letters 23 Probability Theory and Related Fields 22 Communications in Nonlinear Science and Numerical Simulation 20 Archiv der Mathematik 20 Acta Mathematica Hungarica 20 Revista Matemática Iberoamericana 20 Journal de Mathématiques Pures et Appliquées. Neuvième Série 20 Annales Academiae Scientiarum Fennicae. Mathematica 19 Theoretical Computer Science 17 The Annals of Probability 17 Geometriae Dedicata 17 Discrete and Continuous Dynamical Systems 17 Dynamical Systems 17 Mediterranean Journal of Mathematics 16 Physics Letters. A 16 Inventiones Mathematicae 16 Results in Mathematics 16 Physica D 15 Journal of Differential Equations 15 Mathematische Annalen 15 Bernoulli 15 Comptes Rendus. Mathématique. Académie des Sciences, Paris 15 Stochastics and Dynamics 14 Rocky Mountain Journal of Mathematics 14 Annales de l’Institut Fourier 14 Journal of Combinatorial Theory. Series A 14 Journal of Geometry 14 Journal of the London Mathematical Society. Second Series 14 Geometric and Functional Analysis. GAFA 14 Aequationes Mathematicae 13 Advances in Applied Mathematics 13 Science China. Mathematics 12 Duke Mathematical Journal 12 Real Analysis Exchange 12 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques 12 Indagationes Mathematicae. New Series 12 Wuhan University Journal of Natural Sciences (WUJNS) 12 Journal of the European Mathematical Society (JEMS) 11 Advances in Applied Probability 11 Arkiv för Matematik 11 Bulletin of the American Mathematical Society. New Series 11 Bulletin des Sciences Mathématiques 11 Discrete and Continuous Dynamical Systems. Series S 11 Annales Fennici Mathematici 10 Bulletin of the Australian Mathematical Society 10 Proceedings of the Edinburgh Mathematical Society. Series II 10 Science in China. Series A 10 St. Petersburg Mathematical Journal 10 International Journal of Number Theory 10 Complex Analysis and Operator Theory 9 American Mathematical Monthly 9 Journal of Mathematical Physics 9 Journal of Computational and Applied Mathematics 9 Acta Mathematicae Applicatae Sinica. English Series 9 Constructive Approximation 9 Potential Analysis 9 Calculus of Variations and Partial Differential Equations 9 Nonlinear Dynamics 9 Annals of Mathematics. Second Series 8 Archive for Rational Mechanics and Analysis 8 Annali di Matematica Pura ed Applicata. Serie Quarta 8 Bulletin of the London Mathematical Society 8 Zeitschrift für Analysis und ihre Anwendungen 8 Acta Applicandae Mathematicae 8 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 8 Journal of the American Mathematical Society 8 Journal of Dynamics and Differential Equations 8 Conformal Geometry and Dynamics ...and 449 more Serials all top 5 Cited in 59 Fields 2,234 Measure and integration (28-XX) 848 Dynamical systems and ergodic theory (37-XX) 564 Probability theory and stochastic processes (60-XX) 496 Number theory (11-XX) 273 Real functions (26-XX) 264 Convex and discrete geometry (52-XX) 251 Harmonic analysis on Euclidean spaces (42-XX) 222 Partial differential equations (35-XX) 161 Combinatorics (05-XX) 155 Computer science (68-XX) 143 General topology (54-XX) 140 Functions of a complex variable (30-XX) 126 Functional analysis (46-XX) 96 Operator theory (47-XX) 90 Statistical mechanics, structure of matter (82-XX) 86 Statistics (62-XX) 84 Differential geometry (53-XX) 83 Calculus of variations and optimal control; optimization (49-XX) 69 Numerical analysis (65-XX) 68 Potential theory (31-XX) 62 Mathematical logic and foundations (03-XX) 60 Ordinary differential equations (34-XX) 59 Quantum theory (81-XX) 53 Information and communication theory, circuits (94-XX) 52 Geometry (51-XX) 49 Mechanics of deformable solids (74-XX) 47 Approximations and expansions (41-XX) 45 Fluid mechanics (76-XX) 45 Operations research, mathematical programming (90-XX) 44 Biology and other natural sciences (92-XX) 42 Global analysis, analysis on manifolds (58-XX) 36 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 34 Group theory and generalizations (20-XX) 28 Linear and multilinear algebra; matrix theory (15-XX) 27 Manifolds and cell complexes (57-XX) 26 Abstract harmonic analysis (43-XX) 22 Topological groups, Lie groups (22-XX) 22 Difference and functional equations (39-XX) 21 Systems theory; control (93-XX) 18 Integral transforms, operational calculus (44-XX) 16 Relativity and gravitational theory (83-XX) 14 Algebraic geometry (14-XX) 14 Special functions (33-XX) 13 General and overarching topics; collections (00-XX) 13 Several complex variables and analytic spaces (32-XX) 13 Mechanics of particles and systems (70-XX) 12 Sequences, series, summability (40-XX) 10 Algebraic topology (55-XX) 10 Optics, electromagnetic theory (78-XX) 10 Geophysics (86-XX) 9 Integral equations (45-XX) 8 Classical thermodynamics, heat transfer (80-XX) 4 Astronomy and astrophysics (85-XX) 3 History and biography (01-XX) 3 Order, lattices, ordered algebraic structures (06-XX) 2 Field theory and polynomials (12-XX) 2 Commutative algebra (13-XX) 2 Category theory; homological algebra (18-XX) 1 Nonassociative rings and algebras (17-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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