Displaying similar documents to “Equidistribution of Small Points, Rational Dynamics, and Potential Theory”

Embedding theorems for Müntz spaces

Isabelle Chalendar, Emmanuel Fricain, Dan Timotin (2011)

Annales de l’institut Fourier

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We discuss boundedness and compactness properties of the embedding M Λ 1 ⊂ L 1 ( μ ) , where M Λ 1 is the closed linear span of the monomials x λ n in L 1 ( [ 0 , 1 ] ) and μ is a finite positive Borel measure on the interval [ 0 , 1 ] . In particular, we introduce a class of “sublinear” measures and provide a rather complete solution of the embedding problem for the class of quasilacunary sequences Λ . Finally, we show how one can recapture some of Al Alam’s results on boundedness and the essential norm of weighted composition operators...

A.e. convergence of spectral sums on Lie groups

Christopher Meaney, Detlef Müller, Elena Prestini (2007)

Annales de l’institut Fourier

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Let ℒ be a right-invariant sub-Laplacian on a connected Lie group G , and let S R f : = ∫ 0 R d E λ f , R ≥ 0 , denote the associated “spherical partial sums,” where ℒ = ∫ 0 ∞ λ d E λ is the spectral resolution of ℒ . We prove that S R f ( x ) converges a.e. to f ( x ) as R → ∞ under the assumption log ( 2 + ℒ ) f ∈ L 2 ( G ) .

On the mean values of an analytic function.

G. S. Srivastava, Sunita Rani (1992)

Annales Polonici Mathematici

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Let f(z), z = r e i θ , be analytic in the finite disc |z| < R. The growth properties of f(z) are studied using the mean values I δ ( r ) and the iterated mean values N δ , k ( r ) of f(z). A convexity result for the above mean values is obtained and their relative growth is studied using the order and type of f(z).