Spectra of weighted composition operators with automorphic symbols

Olli Hyvärinen, Mikael Lindström*, Ilmari Nieminen, Erno Saukko

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

35 Citations (Scopus)

Abstract

Let φ be an automorphism of the open unit disc D. For such φ, we investigate the spectra of invertible weighted composition operators uCφ acting on a wide class of analytic function spaces; this class contains, for example, Hardy spaces Hp(D), weighted Bergman spaces Aαp(D), and weighted Banach spaces of H-type. We present new techniques for deducing the spectrum and for calculating the spectral radius of uCφ. We also characterize the Fredholmness of weighted composition operators on Hp(D) and Aαp(D).

Original languageEnglish
Pages (from-to)1749-1777
Number of pages29
JournalJournal of Functional Analysis
Volume265
Issue number8
DOIs
Publication statusPublished - 15 Oct 2013
MoE publication typeA1 Journal article-refereed

Keywords

  • Automorphism
  • Fredholm operator
  • Hardy spaces
  • Spectrum
  • Weighted Banach spaces of H-type
  • Weighted Bergman spaces
  • Weighted composition operator

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