Displaying similar documents to “Constructions of smooth and analytic cocycles over irrational circle rotations”

Continued fractions and the Gauss map.

Bates, Bruce, Bunder, Martin, Tognetti, Keith (2005)

Acta Mathematica Academiae Paedagogicae Nyí regyháziensis. New Series [electronic only]

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The fractional dimensional theory in Lüroth expansion

Luming Shen, Kui Fang (2011)

Czechoslovak Mathematical Journal

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It is well known that every x ∈ ( 0 , 1 ] can be expanded to an infinite Lüroth series in the form of x = 1 d 1 ( x ) + ⋯ + 1 d 1 ( x ) ( d 1 ( x ) - 1 ) ⋯ d n - 1 ( x ) ( d n - 1 ( x ) - 1 ) d n ( x ) + ⋯ , where d n ( x ) ≥ 2 for all n ≥ 1 . In this paper, sets of points with some restrictions on the digits in Lüroth series expansions are considered. Mainly, the Hausdorff dimensions of the Cantor sets F φ = { x ∈ ( 0 , 1 ] : d n ( x ) ≥ φ ( n ) , ∀ n ≥ 1 } are completely determined, where φ is an integer-valued function defined on ℕ , and φ ( n ) → ∞ as n → ∞ .

King type modification of q -Bernstein-Schurer operators

Mei-Ying Ren, Xiao-Ming Zeng (2013)

Czechoslovak Mathematical Journal

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Very recently the q -Bernstein-Schurer operators which reproduce only constant function were introduced and studied by C. V. Muraru (2011). Inspired by J. P. King, Positive linear operators which preserve x 2 (2003), in this paper we modify q -Bernstein-Schurer operators to King type modification of q -Bernstein-Schurer operators, so that these operators reproduce constant as well as quadratic test functions x 2 and study the approximation properties of these operators. We establish a convergence...