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Concrete Operators

Ed. by Ross, William / Mashreghi, Javad

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Mathematical Citation Quotient (MCQ) 2017: 0.34

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2299-3282
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Weighted integral Hankel operators with continuous spectrum

Emilio Fedele
  • Department of Mathematics, King’s College London, Strand, London, WC2R 2LS, United Kingdom of Great Britain and Northern Ireland
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/ Alexander Pushnitski
  • Corresponding author
  • Department of Mathematics, King’s College London, Strand, London, WC2R 2LS, United Kingdom of Great Britain and Northern Ireland
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Published Online: 2017-10-31 | DOI: https://doi.org/10.1515/conop-2017-0009

Abstract

Using the Kato-Rosenblum theorem, we describe the absolutely continuous spectrum of a class of weighted integral Hankel operators in L2(ℝ+). These self-adjoint operators generalise the explicitly diagonalisable operator with the integral kernel sαtα(s + t)-1-2α, where α > -1/2. Our analysis can be considered as an extension of J. Howland’s 1992 paper which dealt with the unweighted case, corresponding to α = 0.

Keywords: Weighted Hankel operators; Absolutely continuous spectrum; Carleman operator

MSC 2010: 47B35

References

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About the article

Received: 2017-02-24

Accepted: 2017-09-25

Published Online: 2017-10-31

Published in Print: 2017-10-26


Citation Information: Concrete Operators, Volume 4, Issue 1, Pages 121–129, ISSN (Online) 2299-3282, DOI: https://doi.org/10.1515/conop-2017-0009.

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© 2017. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License. BY-NC-ND 4.0

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