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Warianty tytułu
Języki publikacji
Abstrakty
For a bounded linear operator on a Banach space, we study approximation of the spectrum and pseudospectra in the Hausdorff distance. We give sufficient and necessary conditions in terms of pointwise convergence of appropriate spectral quantities.
Słowa kluczowe
Czasopismo
Rocznik
Tom
Strony
101--108
Opis fizyczny
Bibliogr. 14 poz.
Twórcy
autor
- TU Hamburg, Institute of Mathematics, Am Schwarzenberg - Campus 1, 21073 Hamburg, Germany
autor
- TU Hamburg, Institute of Mathematics, Am Schwarzenberg - Campus 1, 21073 Hamburg, Germany
Bibliografia
- [1] S.N. Chandler-Wilde, R. Chonchaiya, M. Lindner, On spectral inclusion sets and computing the spectra and pseudospectra of bounded linear operators, in preparation.
- [2] M.J. Colbrook, Pseudoergodic operators and periodic boundary conditions, Math. Comp. 89 (2020), no. 322, 737–766.
- [3] E.B. Davies, E. Shargorodsky, Level sets of the resolvent norm of a linear operator revisited, Mathematika 62 (2015), no. 1, 243–265.
- [4] M.M. Day, Some more uniformly convex spaces, Bull. Amer. Math. Soc. 47 (1941), 504–507.
- [5] F. Gabel, D. Gallaun, J. Grossmann, M. Lindner, R. Ukena, Spectral approximation of generalized Schrödinger operators via approximation of subwords, in preparation.
- [6] J. Globevnik, Norm-constant analytic functions and equivalent norms, Illinois J. Math. 20 (1976), no. 3, 503–506.
- [7] R. Hagen, S. Roch, B. Silbermann, C∗-Algebras and Numerical Analysis, Monographs and Textbooks in Pure and Applied Mathematics, vol. 236, Marcel Dekker, Inc., New York, Basel, 2001.
- [8] R. Hagger, M. Lindner, M. Seidel, Essential pseudospectra and essential norms of band-dominated operators, J. Math. Anal. Appl. 437 (2016), no. 1, 255–291.
- [9] M. Lindner, D. Schmeckpeper, How stability indicators determine asymptotics of resolvents, condition numbers and pseudospectra, in preparation.
- [10] M. Lindner, M. Seidel, An affirmative answer to a core issue on limit operators, J. Funct. Anal. 267 (2014), no. 3, 901–917.
- [11] E. Shargorodsky, On the level sets of the resolvent norm of a linear operator, Bull. London Math. Soc. 40 (2008), no. 3, 493–504.
- [12] E. Shargorodsky, On the definition of pseudospectra, Bull. London Math. Soc. 41 (2009), no. 3, 524–534.
- [13] E. Shargorodsky, S. Shkarin, The level sets of the resolvent norm and convexity properties of Banach spaces, Arch. Math. 93 (2009), no. 1, 59–66.
- [14] L.N. Trefethen, M. Embree, Spectra and Pseudospectra: The Behavior of Nonnormal Matrices and Operators, Princeton Univ. Press, Princeton, NJ, 2005.
Uwagi
Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023)
Typ dokumentu
Bibliografia
Identyfikator YADDA
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