On a function that realizes the maximal spectral type

• Autorzy: Krzysztof M. Frączek
• Języki publikacji: EN

Abstrakty

EN

We show that for a unitary operator U on $L^2(X,μ)$, where X is a compact manifold of class $C^r$, $r ∈ ℕ ∪ {∞,ω}$, and μ is a finite Borel measure on X, there exists a $C^r$ function that realizes the maximal spectral type of U.

Kategorie tematyczne

• 47B15: Hermitian and normal operators (spectral measures, functional calculus, etc.)
• 28D05: Measure-preserving transformations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1997
• Tom: 124
• Numer: 1
• Strony: 1-7

Daty

wydano

1997

otrzymano

1995-12-05

poprawiono

1996-12-03

Twórcy

autor

Krzysztof M. Frączek

• Department of Mathematics and Computer Science, Nicholas Copernicus University, Chopina 12/18, 87-100 Toruń, Poland

Bibliografia

• [1] V. M. Alexeyev, Existence of a bounded function of the maximal spectral type, Ergodic Theory Dynam. Systems 2 (1982), 259-261.
• [2] S. Bochner and W. T. Martin, Several Complex Variables, Princeton Univ. Press, Princeton, 1948.
• [3] N. Dunford and T. Schwartz, Linear Operators, Wiley-Interscience, 1971.
• [4] H. Grauert, On Levi's problem and the imbedding of real-analytic manifolds, Ann. of Math. 68 (1958), 460-472.
• [5] W. Parry, Topics in Ergodic Theory, Cambridge Univ. Press, Cambridge, 1981.