ON THE DENSITY OF LAGUERRE FUNCTIONS IN SOME BANACH FUNCTION SPACES

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Abstract

Let lambda > 0 and Phi(lambda) := {phi(1,lambda), phi(2,lambda), ...} be the system of dilated Laguerre functions. We show that if L-1 (R+) boolean AND L-infinity(R+) is embedded into a separable Banach function space X(R+), then the linear span of Phi(lambda) is dense in X(R+). This implies that the linear span of Phi(lambda) is dense in every separable rearrangement-invariant space X(R+) and in every separable variable Lebesgue space L-p(.)(R+).
Original languageEnglish
Pages (from-to)37-45
Number of pages9
JournalJournal of Inequalities and Special Functions
Volume13
Issue number2
DOIs
Publication statusPublished - 2022

Keywords

  • Laguerre functions
  • Banach function space
  • rearrangement-invariant space
  • variable Lebesgue space

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