The logarithmic asymptotic expansions for the norms of evaluation functionals

Dovgoshei A., ABDULLAYEV F., Kucukaslan M.

Siberian Mathematical Journal, cilt.46, sa.4, ss.613-622, 2005 (SCI-Expanded, Scopus) identifier

  • Yayın Türü: Makale / Derleme
  • Cilt numarası: 46 Sayı: 4
  • Basım Tarihi: 2005
  • Doi Numarası: 10.1007/s11202-005-0062-6
  • Dergi Adı: Siberian Mathematical Journal
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.613-622
  • Anahtar Kelimeler: Evaluation functionals, General orthogonal polynomials, Green's function, Irregularity points for the Dirichlet problem, Logarithmic asymptotic expansion
  • Uşak Üniversitesi Adresli: Hayır

Özet

Let μ be a compactly supported finite Borel measure in ℂ, and let Πn be the space of holomorphic polynomials of degree at most n furnished with the norm of L 2(μ). We study the logarithmic asymptotic expansions of the norms of the evaluation functionals that relate to polynomials p Πn their values at a point z ∈ ℂ. The main results demonstrate how the asymptotic behavior depends on regularity of the complement of the support of μ and the Stahl-Totik regularity of the measure. In particular, we study the cases of pointwise and μ-a.e. convergence as n → ∞. © 2005 Springer Science+Business Media, Inc.