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Multiplicity theory and the outer boundary


Author: John S. Spraker
Journal: Proc. Amer. Math. Soc. 112 (1991), 391-392
MSC: Primary 47B38; Secondary 47B15
DOI: https://doi.org/10.1090/S0002-9939-1991-1062837-2
MathSciNet review: 1062837
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Abstract: Let $ f$ be a conformal map from the unit disk onto a simply-connected region $ R$. Multiplication by $ f$ on $ {L^2}$ is a normal operator. In this paper it is shown that the outer boundary of $ R$ is a set of multiplicity one for this operator.


References [Enhancements On Off] (What's this?)

  • [1] M. B. Abrahamse, Multiplication operators, Lecture Notes in Math., vol. 693, Springer-Verlag, Berlin, 1978, pp. 17-36. MR 526530 (80b:47042)
  • [2] M. B. Abrahamse and T. L. Kriete, The spectral multiplicity of a multiplication operator, Indiana Univ. Math. J. 22 (1973), 845-857. MR 0320797 (47:9331)
  • [3] T. L. Kriete, An elementary approach to the multiplicity theory of multiplication operators, Rocky Mountain J. Math. 16 (1986), 23-33. MR 829193 (87e:47035)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1991-1062837-2
Keywords: Multiplicity, multiplication operator
Article copyright: © Copyright 1991 American Mathematical Society

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