Explicit Salem sets in R2

Advances in Mathematics - Tập 311 - Trang 634-648 - 2017
Kyle Hambrook1
1Department of Mathematics, University of Rochester, Rochester, NY 14627, USA

Tài liệu tham khảo

Beresnevich, 2006, A mass transference principle and the Duffin–Schaeffer conjecture for Hausdorff measures, Ann. of Math. (2), 164, 971, 10.4007/annals.2006.164.971 Beresnevich, 2006, Schmidt's theorem, Hausdorff measures, and slicing, Int. Math. Res. Not., 10.1155/IMRN/2006/48794 Besicovitch, 1934, Sets of fractional dimension (IV): on rational approximation to real numbers, J. Lond. Math. Soc., 9, 126, 10.1112/jlms/s1-9.2.126 Bluhm, 1996, Random recursive construction of Salem sets, Ark. Mat., 34, 51, 10.1007/BF02559506 Bluhm, 1998, On a theorem of Kaufman: Cantor-type construction of linear fractal Salem sets, Ark. Mat., 36, 307, 10.1007/BF02384771 Bovey, 1986, The Hausdorff dimension of systems of linear forms, Acta Arith., 45, 337, 10.4064/aa-45-4-337-358 Chen Eggleston, 1951, Sets of fractional dimensions which occur in some problems of number theory, Proc. Lond. Math. Soc., 54, 42 Ekström, 2015, On the Fourier dimension and a modification, J. Fractal Geom., 2, 309, 10.4171/JFG/23 Ekström, 2016, Fourier dimension of random images, Ark. Mat., 54, 455, 10.1007/s11512-016-0237-3 Falconer, 1986, vol. 85 Fraser, 2014, On Fourier analytic properties of graphs, Int. Math. Res. Not., 10, 2730, 10.1093/imrn/rnt015 Frostman, 1935, Potentiel d'équilibre et capacité des ensembles avec quelques applications à la théorie des fonctions, Meddel. Lunds Univ. Math. Sem., 3, 1 Gatesoupe, 1967, Sur un théorème de R. Salem, Bull. Sci. Math. (2), 91, 125 Hambrook Hardy, 2008 Hurwitz, 1898, Über die Composition der quadratischen Formen von beliebig vielen Variabeln, Goett. Nachr., 309 Hurwitz, 1923, Über die Komposition der quadratischen Formen, Math. Ann., 88, 1, 10.1007/BF01448439 Jarník, 1929, Diophantischen Approximationen und Hausdorffsches Mass, Mat. Sb., 36, 371 Kahane, 1966, Images browniennes des ensembles parfaits, C. R. Acad. Sci. Paris Sér. A-B, 263, A613 Kahane, 1966, Images d'ensembles parfaits par des séries de Fourier gaussiennes, C. R. Acad. Sci. Paris Sér. A-B, 263, A678 Kahane, 1985 Kaufman, 1981, On the theorem of Jarník and Besicovitch, Acta Arith., 39, 265, 10.4064/aa-39-3-265-267 Kervaire, 1958, Non-parallelizability of the n-sphere for n>7, Proc. Natl. Acad. Sci., 44, 280, 10.1073/pnas.44.3.280 Łaba, 2009, Arithmetic progressions in sets of fractional dimension, Geom. Funct. Anal., 19, 429, 10.1007/s00039-009-0003-9 Landau, 1903, Neuer Beweis des Primzahlsatzes und Beweis des Primidealsatzes, Math. Ann., 56, 645, 10.1007/BF01444310 Mattila, 1995, Geometry of Sets and Measures in Euclidean Spaces, vol. 44 Mattila, 2015 Milnor, 1958, Some consequences of a theorem of Bott, Ann. of Math. (2), 68, 444, 10.2307/1970255 Montgomery, 2007 Salem, 1951, On singular monotonic functions whose spectrum has a given Hausdorff dimension, Ark. Mat., 1, 353, 10.1007/BF02591372 Shmerkin Wolff, 2003