Extendible bases and Kolmogorov problem on asymptotics of entropy and widths of some class of analytic functions

  title={Extendible bases and Kolmogorov problem on asymptotics of entropy and widths of some class of analytic functions},
  author={Vyacheslav Zakharyuta},
  journal={Annales de la Facult{\'e} des Sciences de Toulouse},
  • V. Zakharyuta
  • Published 2011
  • Mathematics
  • Annales de la Faculté des Sciences de Toulouse
— Let K be a compact set in an open set D on a Stein manifold Ω of dimension n. We denote by H∞ (D) the Banach space of all bounded and analytic in D functions endowed with the uniform norm and by AK a compact subset of the space C (K) consisted of all restrictions of functions from the unit ball BH∞(D). In 1950ies Kolmogorov posed a problem: does Hε ( AK ) ∼ τ ( ln 1 ε )n+1 , ε→ 0, whereHε ( AK ) is the ε-entropy of the compact AK . We give here a survey of results concerned with this problem… 

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