Research papers of Tamás Keleti

  1. Richárd Balka, KT: New Hausdorff type dimensions and optimal bounds for bilipschitz invariant dimensions,
    arXiv:2312.06456.

  2. Richárd Balka, KT: Lipschitz images and dimensions, to appear in Advances in Mathematics,
    arXiv:2308.02639.

  3. TK and András Máthé: Equivalences between different forms of the Kakeya conjecture and duality of Hausdorff and packing dimensions for additive complements,
    arXiv:2203.15731.

  4. Alex Burgin, Samuel Goldberg, TK, Connor MacMahon, Xianzhi Wang: Large sets avoiding infinite arithmetic / geometric progressions, Real Analysis Exchange 48 (2023), 351-364.
    arXiv:2210.09284.

  5. TK, Stephen Lacina, Changshuo Liu, Mengzhen Liu, José Ramón Tuirán Rengel: Tiling of rectangles via Diophantine approximation, Discrete Mathematics 346 (2023), 113442.
    The final publication is freely available here.
    pdf

  6. James Cumberbatch, TK, Jialin Zhang: Hausdorff dimension of union of lines that cover a curve, to appear in Pure and Applied Functional Analysis.
    arXiv:2107.07995.

  7. Kornélia Héra, TK and András Máthé: A Fubini-type theorem for Hausdorff dimension, Journal d'Analyse Mathématique (2023).
    The final publication is freely available here.
    arXiv:2106.09661.

  8. Zoltán Buczolich, Esa Järvenpää, Maarit Järvenpää, TK and Tuomas Pöyhtäri: Fractal percolation is unrectifiable, Advances in Mathematics 390 (2021) 107906.
    arXiv:1910.11796.
    The final publication is freely availble at https://doi.org/10.1016/j.aim.2021.107906.

  9. Frank Coen, Nate Gillman, TK, Dylan King and Jennifer Zhu: Large sets with small injective projections, Annales Fennici Mathematici 46 (2021), 683-702.
    arXiv:1906.06288.
    The final publication is freely available at afm.journal.fi.

  10. TK and Pablo Shmerkin: New bounds on the dimension of planar distance sets, Geom. Funct. Anal. 29 (2019), 1886-1948.
    arXiv:1801.08745.

  11. Kornélia Héra, TK and András Máthé: Hausdorff dimension of union of affine subspaces, J. Fractal Geom. 6 (2019), 263-284.
    arXiv:1701.02299.

  12. Alan Chang, Marianna Csörnyei, Kornélia Héra and TK: Small unions of affine subspaces and skeletons via Baire category, Adv. Math. 328 (2018), 801-821.
    arXiv:1701.01405.

  13. TK: Small union with large set of centers, Recent Developments in Fractals and Related Fielsds Conference on Fractals and Related Fields III, île de Porquerolles, France, 2015, J. Barral & S. Seuret (Eds.), Birkhäuser Basel, 2017, 189-206.
    arXiv:1701.027622

  14. TK, Máté Matolcsi, Fernando Mário de Oliveira Filho and Imre Z. Ruzsa: Better bounds for planar sets avoiding unit distances, Discrete & Computational Geometry 55 (2016), 642-661.
    arXiv:1501.00168
    The final publication is available at link.springer.com.

  15. TK: Are lines much bigger than line segments?, Proc. Amer. Math. Soc. 144 (2016), 1535-1541.
    arXiv:1409.5992
    The final publication is available at www.ams.org.

  16. TK, Dániel T. Nagy and Pablo Shmerkin: Squares and their centers, Journal d'Analyse Mathematique 134 (2018), 643-669.
    arXiv:1428.1029
    The final publication is available at link.springer.com.

  17. Márton Elekes and TK: Decomposing the real line into Borel sets closed under addition, Mathematical Logic Quarterly 61 (2015), 466-473.
    arXiv:1406.0701
    The final publication is available at onlinelibrary.wiley.com.

  18. TK, András Máthé and Ondřej Zindulka: Hausdorff dimension of metric spaces and Lipschitz maps onto cubes, Int. Math. Res. Notices 2014 (2014), 289-302.
    free access to the full text
    arXiv:1203.0686

  19. Esa Järvenpää, Maarit Järvenpää and TK: Hausdorff dimension and non-degenerate families of projections, J Geom Anal 24 (2014), 2020-2034
    arXiv:1203.5296
    The final publication is available at link.springer.com.

  20. Márton Elekes, TK and András Máthé: Reconstructing geometric objects from the measures of their intersections with test sets, J. Fourier Anal. Appl. 19 (2013) 545-576.
    arXiv:1109.6169
    The final publication is available at link.springer.com.

  21. Viktor Harangi, TK, Gergely Kiss, Péter Maga, András Máthé, Pertti Mattila and Balázs Strenner: How large dimension guarantees a given angle?, Monatsh. Math. 171 (2013) 169-187.
    arXiv:1101.1426
    The final publication is available at link.springer.com.

  22. Esa Järvenpää, Maarit Järvenpää, TK and András Máthé: Continuously parametrized Besicovitch sets in R^n, Ann. Acad. Sci. Fenn. Math. 36 (2011), 411-421.
    pdf

  23. TK and Elliot Paquette: The trouble with the Koch curve built from n-gons , Amer. Math. Monthly 117 (2010), no. 2, 124-137.
    pdf, an illustration

  24. Márton Elekes, TK and András Máthé: Self-similar and self-affine sets; measure of the intersection of two copies, Ergodic Theory Dynam. Systems 117 (2010), no. 2, 124-137.
    pdf, ps

  25. TK: Construction of 1-dimensional subsets of the reals not containing similar copies of given patterns, Anal. PDE 1 (2008), no. 1, 29--33.
    pdf

  26. Bálint Farkas, Viktor Harangi, TK and Szilárd György Révész: Invariant decomposition of functions with respect to commuting invertible transformations , Proc. Amer. Math Soc. 136 (2008), 1325-1336.
    pdf

  27. TK: Periodic decomposition of measurable integer valued functions, J. Math. Anal. Appl. 337 (2008), 1394-1403.
    dvi, pdf, ps

  28. Gyula Károlyi, TK, Géza Kós and Imre Z. Ruzsa: Periodic decomposition of integer valued functions, Acta Math. Hungar. 119 (2008), no. 3, 227--242..
    dvi, pdf, ps

  29. TK and Mihalis Kolountzakis: On the determination of sets by their triple correlation in finite cyclic groups, Online Journal of Analytic Combinatorics 1 (2006), #4.
    dvi, pdf, ps

  30. TK: When is the modified von Koch snowflake non-self-intersecting?, Fractals 14 (2006), No. 3, 245-249.
    pdf, ps

  31. Márton Elekes and TK: Is Lebesgue measure the only sigma-finite invariant Borel measure?, J. Math. Anal. Appl. 321 (2006) 445-451.
    dvi, pdf, ps

  32. Márton Elekes and TK: Borel sets which are null or non-sigma-finite for every translation invariant measure, Adv. Math. 201 (2006), 102-115.
    dvi, pdf, ps

  33. Petr Holicky and TK: Borel classes of sets of extreme and exposed points in R^n , Proc. Amer. Math. Soc. 133 (2005), no. 6, 1851-1859..
    dvi, pdf, ps

  34. TK and Tamás Mátrai: A nowhere convergent series of functions which is somewhere convergent after a typical change of signs, Real Analysis Exchange 29 (2003/04), no. 2, 891-894.
    pdf, ps

  35. Udayan B. Darji and TK: Covering the real line with translates of a compact set, Proc. Amer. Math. Soc. 131 (2003), 2593-2596.
    dvi, pdf, ps

  36. Márton Elekes, TK and Vilmos Prokaj: The composition of derivatives has a fixed point, Real Analysis Exchange 27 (2001/02), 131-140.
    dvi, pdf, ps

  37. Miklós Abért and TK: Shuffle the plane, Proc. Amer. Math. Soc. 130 (2002), 549-553.
    dvi, pdf, ps

  38. TK and David Preiss: The balls do not generate all Borel sets using complements and countable disjoint unions, Math. Proc. Cambridge Philos. Soc. 128 (2000), no. 3, 539-547.
    dvi, pdf, ps

  39. TK: The Dynkin system generated by the large balls of R^n, Real Anal. Exchange 24 (1998/99), no. 2, 859-866.
    dvi, pdf, ps

  40. TK: Density and covering properties of intervals of R^n, Mathematika 47 (2000), 229-242.
    dvi, pdf, ps

  41. TK: A covering property of some classes of sets in R^n, Acta Univ. Carolin. Math. Phys. 39 (1998), no. 1-2, 111-118.
    dvi, pdf, ps

  42. TK: A 1-dimensional subset of the reals that intersects each of its translates in at most a single point, Real Anal. Exchange 24 (1998/99), no. 2, 843--844.
    dvi, pdf, ps

  43. TK: Difference functions of periodic measurable functions, Fund. Math. 157 (1998), no. 1, 15--32.
    dvi, pdf, ps

  44. TK: Periodic ${\rm Lip}\sp \alpha$ functions with ${\rm Lip}\sp \beta$ difference functions Colloq. Math. 76 (1998), no. 1, 99--103.
    dvi, pdf, ps

  45. TK: Periodic $L\sb p$ functions with $L\sb q$ difference functions, Real Anal. Exchange 23 (1997/98), no. 2, 431--440.
    dvi, pdf, ps

  46. TK: On the differences and sums of periodic measurable functions, Acta Math. Hungar. 75 (1997), no. 4, 279--286.
    dvi, pdf, ps

  47. TK: Difference functions of periodic measurable functions, PhD dissertation, Eötvös Loránd University, Budapest, 1996.
    pdf, ps

  48. TK: A peculiar set in the plane constructed by Vitushkin, Ivanov and Melnikov, Real Anal. Exchange 20 (1994/95), no. 1, 291--312.
    pdf, ps

  49. TK: The mountain climbers' problem, Proc. Amer. Math. Soc. 117 (1993), no. 1, 89--97.
    dvi, pdf, ps