Rational Approximation on Product Sets
نویسندگان
چکیده
منابع مشابه
Sets of exact approximation order by rational numbers III
For a function Ψ : R>0 → R>0, let Exact(Ψ) be the set of real numbers that are approximable by rational numbers to order Ψ, but to no order cΨ with 0 < c < 1. When Ψ is non-increasing and satisfies Ψ(x) = o(x−2), we establish that Exact(Ψ) has Hausdorff dimension 2/λ, where λ is the lower order at infinity of the function 1/Ψ. Furthermore, we study the set Exact(Ψ) when Ψ is not assumed to be n...
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Let S∞ = A∞ × B∞ be a self-similar product Cantor set in the complex plane, defined via S∞ = ⋃L j=1 Tj(S∞), where Tj : C→ C have the form Tj(z) = 1 Lz+zj and {z1, . . . , zL} = A+iB for some A,B ⊂ R with |A|, |B| > 1 and |A||B| = L. Let SN be the L−N -neighbourhood of S∞, or equivalently (up to constants), its N -th Cantor iteration. We are interested in the asymptotic behaviour as N → ∞ of the...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1974
ISSN: 0002-9947
DOI: 10.2307/1996998