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Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.79.

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On the Solvability Complexity Index, the $n$-pseudospectrum and approximations of spectra of operators
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by Anders C. Hansen PDF
J. Amer. Math. Soc. 24 (2011), 81-124 Request permission


We show that it is possible to compute spectra and pseudospectra of linear operators on separable Hilbert spaces given their matrix elements. The core in the theory is pseudospectral analysis and in particular the $n$-pseudospectrum and the residual pseudospectrum. We also introduce a new classification tool for spectral problems, namely, the Solvability Complexity Index. This index is an indicator of the “difficultness” of different computational spectral problems.
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Additional Information
  • Anders C. Hansen
  • Affiliation: Department of Applied and Computational Mathematics, California Institute of Technology, Pasadena, California 91125
  • Address at time of publication: Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom
  • Email:
  • Received by editor(s): August 28, 2009
  • Published electronically: July 12, 2010
  • © Copyright 2010 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: J. Amer. Math. Soc. 24 (2011), 81-124
  • MSC (2010): Primary 47A10; Secondary 47A75, 46L05, 81Q10, 81Q12, 65J10
  • DOI:
  • MathSciNet review: 2726600