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Norms, Condition Numbers and Pseudospectra of Convolution Type Operators on Intervals

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Part of the Operator Theory: Advances and Applications book series (OT,volume 259)

Abstract

The results in this paper describe the asymptotic behavior of convolution type operators on finite intervals as the length of these intervals tends to infinity. The family of operators under consideration here is generated (among others) by Fourier convolutions with slowly oscillating, almost periodic, bounded and uniformly continuous, and quasi-continuous multipliers, as well as operators of multiplication by slowly oscillating, almost periodic, and piecewise continuous functions. The focus is on the convergence of norms, condition numbers and pseudospectra.

Keywords

  • Operator sequence
  • convolution operator
  • Fourier multiplier
  • finite section method
  • condition number
  • pseudospectrum

Mathematics Subject Classification (2010). 65R20, 47G10, 47B35.

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Correspondence to Markus Seidel .

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Seidel, M. (2017). Norms, Condition Numbers and Pseudospectra of Convolution Type Operators on Intervals. In: Bini, D., Ehrhardt, T., Karlovich, A., Spitkovsky, I. (eds) Large Truncated Toeplitz Matrices, Toeplitz Operators, and Related Topics. Operator Theory: Advances and Applications, vol 259. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-49182-0_27

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