Opuscula Math. 41, no. 6 (2021), 747-754

Opuscula Mathematica

Generalized powers and measures

Zbigniew Burdak
Marek Kosiek
Patryk Pagacz
Krzysztof Rudol
Marek Słociński

Abstract. Using the winding of measures on torus in "rational directions" special classes of unitary operators and pairs of isometries are defined. This provides nontrivial examples of generalized powers. Operators related to winding Szegö-singular measures are shown to have specific properties of their invariant subspaces.

Keywords: representing measures, Szegö-singular measure, compatible pair of isometries, spectral measure.

Mathematics Subject Classification: 47B20, 47A13, 47B91.

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  • Krzysztof Rudol (corresponding author)
  • ORCID iD https://orcid.org/0000-0001-7030-653X
  • AGH University of Science and Technology, Faculty of Applied Mathematics, al. Mickiewicza 30, 30-059 Kraków, Poland
  • Communicated by Alexander Gomilko.
  • Received: 2021-07-26.
  • Revised: 2021-08-26.
  • Accepted: 2021-09-15.
  • Published online: 2021-11-29.
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Cite this article as:
Zbigniew Burdak, Marek Kosiek, Patryk Pagacz, Krzysztof Rudol, Marek Słociński, Generalized powers and measures, Opuscula Math. 41, no. 6 (2021), 747-754, https://doi.org/10.7494/OpMath.2021.41.6.747

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