Limit points of eigenvalues of truncated unbounded tridiagonal operators

• Autorzy: E.K. Ifantis , C.G. Kokologiannaki , E. Petropoulou
• Języki publikacji: EN

Abstrakty

EN

Let T be a self-adjoint tridiagonal operator in a Hilbert space H with the orthonormal basis {e n}n=1∞, σ(T) be the spectrum of T and Λ(T) be the set of all the limit points of eigenvalues of the truncated operator T N. We give sufficient conditions such that the spectrum of T is discrete and σ(T) = Λ(T) and we connect this problem with an old problem in analysis.

Słowa kluczowe

EN

Tridiagonal operators; spectrum; limit points of eigenvalues; orthogonal polynomials; continued fractions

Kategorie tematyczne

• 40A15: Convergence and divergence of continued fractions
• 42C05: Orthogonal functions and polynomials, general theory
• 47A10: Spectrum, resolvent

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2007
• Tom: 5
• Numer: 2
• Strony: 335-344

Daty

wydano

2007-06-01

online

2007-06-01

Twórcy

autor

E.K. Ifantis

• University of Patras

autor

C.G. Kokologiannaki

• University of Patras

autor

E. Petropoulou

• University of Patras

Bibliografia

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• [5] E.K. Ifantis and P. Panagopoulos: “Limit points of eigenvalues of truncated tridiagonal operators”, J. Comp. Appl. Math., Vol. 133, (2001), pp. 413–422. http://dx.doi.org/10.1016/S0377-0427(00)00663-4
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• [7] T.J. Stieltjes: “Recherches sur les fractions continues”, Ann. Fac. Sci. Toulouse Mat., Vol. 8, (1894), J1–J122; Vol. 9, (1895), A1–A47; Oeuvres, Vol. 2, (1918), pp. 398–506.
• [8] M.H. Stone: “Linear Transformations in Hilbert space and their Applications to Analysis”, In: Amer. Math. Soc. Colloq. Publ., Vol. 15, Amer. Math. Soc., Providence, R.I. New York, 1932.
• [9] H.S. Wall: “On continued fractions which represent meromorphic functions”, Bull. Amer. Math. Soc., Vol. 39, (1933), pp. 946–952. http://dx.doi.org/10.1090/S0002-9904-1933-05778-6

Identyfikatory

DOI

10.2478/s11533-007-0009-1