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Toeplitz Matrices with Slowly Growing Pseudospectra

In: Factorization, Singular Operators and Related Problems

Author

Listed:
  • Albrecht Böttcher

    (TU Chemnitz, Faculty of Mathematics)

  • Sergei Grudsky

    (Rostov on Don State University, Faculty of Mechanics and Mathematics
    CINVESTAV del I.P.N., Departamento de Matemáticas)

Abstract

Let T(a) be the infinite Toeplitz matrix with the symbol a and let T n (a) denote the n × n principal submatrix of T(a). The pseudospectra of T n (a) are known to converge to the pseudospectrum of T(a) as n → ∞ provided a is piecewise continuous. Only recently, Mark Embree, Nick Trefethen, and one of the authors observed that this convergence may be spectacularly slow in case a has a jump. The main result of this paper says that such a slow convergence of pseudospectra is generic even within the class of continuous symbols.

Suggested Citation

  • Albrecht Böttcher & Sergei Grudsky, 2003. "Toeplitz Matrices with Slowly Growing Pseudospectra," Springer Books, in: Stefan Samko & Amarino Lebre & António F. dos Santos (ed.), Factorization, Singular Operators and Related Problems, pages 43-54, Springer.
    • Handle: RePEc:spr:sprchp:978-94-017-0227-0_4
    DOI: 10.1007/978-94-017-0227-0_4
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