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Spectra of Multiplication Operators in Sobolev Spaces

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Abstract.

Known results on the spectra of matrix multiplication operators in Lp spaces are extended to Sobolev spaces. Here regularity conditions are necessary for the resolvent set to be non-empty. Under certain regularity conditions on the multiplication matrix, the spectrum of the operator is explicitly given in terms of properties of the matrix.

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Authors and Affiliations

  1. School of Mathematics, University of the Witwatersrand, WITS, 2050, Johannesburg, South Africa

    Hannalie Brooks

  2. The John Knopfmacher Centre of Applicable Analysis and Number Theory, School of Mathematics, University of the Witwatersrand, WITS, 2050, Johannesburg, South Africa

    Manfred Möller

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  1. Hannalie Brooks
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  2. Manfred Möller
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Correspondence to Hannalie Brooks.

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Received: April 8, 2009. Revised: July 27, 2009.

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Brooks, H., Möller, M. Spectra of Multiplication Operators in Sobolev Spaces. Results. Math. 55, 281 (2009). https://doi.org/10.1007/s00025-009-0433-6

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  • DOI: https://doi.org/10.1007/s00025-009-0433-6

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