Opuscula Math. 41, no. 6 (2021), 747-754
https://doi.org/10.7494/OpMath.2021.41.6.747
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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- Zbigniew Burdak
https://orcid.org/0000-0002-6097-5761- Department of Applied Mathematics, University of Agriculture, ul. Balicka 253c, 30-198 Kraków, Poland
- Marek Kosiek
- https://orcid.org/0000-0002-1455-6275
- Jagiellonian University, Faculty of Mathematics and Computer Science, ul. Prof. St. Łojasiewicza 6, 30-348 Kraków, Poland
- Patryk Pagacz
- https://orcid.org/0000-0001-9866-1613
- Jagiellonian University, Faculty of Mathematics and Computer Science, ul. Prof. St. Łojasiewicza 6, 30-348 Kraków, Poland
- Krzysztof Rudol (corresponding author)
- https://orcid.org/0000-0001-7030-653X
- AGH University of Science and Technology, Faculty of Applied Mathematics, al. Mickiewicza 30, 30-059 Kraków, Poland
- Marek Słociński
- https://orcid.org/0000-0002-8499-5126
- Jagiellonian University, Faculty of Mathematics and Computer Science, ul. Prof. St. Łojasiewicza 6, 30-348 Kraków, Poland
- Communicated by Alexander Gomilko.
- Received: 2021-07-26.
- Revised: 2021-08-26.
- Accepted: 2021-09-15.
- Published online: 2021-11-29.
