Entire functions of least deviation from zero in generalized Orlicz classes

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Abstract

Some results of S. N. Bernstein about polynomials of least deviation from zero in some weighted spaces L p are generalized to entire functions of exponential type. Suppose that a function ρm belongs to the Cartwright class, is of type m, is positive on the real axis, and let σ ≥ m. Earlier, the authors constructed functions least deviating from zero among entire functions of type σ in the uniform and integral metrics on R with the weights ω = 1/ρm and ω =

Original languageEnglish
Pages (from-to)219-230
Number of pages12
JournalSt. Petersburg Mathematical Journal
Volume30
Issue number2
DOIs
StatePublished - 1 Jan 2019

Scopus subject areas

  • Analysis

Keywords

  • Entire functions of least deviation from zero
  • Orlicz classes
  • Weighted spaces

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