On a function that realizes the maximal spectral type

Krzysztof Frączek

Studia Mathematica (1997)

  • Volume: 124, Issue: 1, page 1-7
  • ISSN: 0039-3223

Abstract

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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.

How to cite

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Frączek, Krzysztof. "On a function that realizes the maximal spectral type." Studia Mathematica 124.1 (1997): 1-7. <http://eudml.org/doc/216395>.

@article{Frączek1997,
abstract = {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.},
author = {Frączek, Krzysztof},
journal = {Studia Mathematica},
keywords = {unitary operator; compact manifold; maximal spectral type},
language = {eng},
number = {1},
pages = {1-7},
title = {On a function that realizes the maximal spectral type},
url = {http://eudml.org/doc/216395},
volume = {124},
year = {1997},
}

TY - JOUR
AU - Frączek, Krzysztof
TI - On a function that realizes the maximal spectral type
JO - Studia Mathematica
PY - 1997
VL - 124
IS - 1
SP - 1
EP - 7
AB - 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.
LA - eng
KW - unitary operator; compact manifold; maximal spectral type
UR - http://eudml.org/doc/216395
ER -

References

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  1. [1] V. M. Alexeyev, Existence of a bounded function of the maximal spectral type, Ergodic Theory Dynam. Systems 2 (1982), 259-261. 
  2. [2] S. Bochner and W. T. Martin, Several Complex Variables, Princeton Univ. Press, Princeton, 1948. Zbl0041.05205
  3. [3] N. Dunford and T. Schwartz, Linear Operators, Wiley-Interscience, 1971. 
  4. [4] H. Grauert, On Levi's problem and the imbedding of real-analytic manifolds, Ann. of Math. 68 (1958), 460-472. Zbl0108.07804
  5. [5] W. Parry, Topics in Ergodic Theory, Cambridge Univ. Press, Cambridge, 1981. Zbl0449.28016

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