Simple eigenvectors of unbounded operators of the type "normal plus compact"

• Autorzy: Gil M.

Identyfikatory

DOI

http://dx.doi.Org/10.7494/OpMath.2015.35.2.161

• Języki publikacji: EN

Abstrakty

EN

The paper deals with operators of the form A = S + B, where B is a compact operator in a Hilbert space H and S is an unbounded normal one in H, having a compact resolvent. We consider approximations of the eigenvectors of A, corresponding to simple eigenvalues by the eigenvectors of the operators An = S + Bn (n = 1, 2,...), where Bn is an n-dimensional operator. In addition, we obtain the error estimate of the approximation.

Słowa kluczowe

EN

Hilbert space; linear operators; eigenvectors; approximation; integro-differential operators; Schatten-von Neumann operators

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2015
• Tom: Vol. 35, no. 2
• Strony: 161--169
• Opis fizyczny: Bibliogr. 16 poz.

Twórcy

autor

Gil M.

• Ben Gurion University of the Negev Department of Mathematics P.O. Box 653, Beer-Sheva 84105, Israel

Bibliografia

• [1] H. Abels, M. Kassmann, The Cauchy problem and the martingale problem for integro-differential operators with non-smooth kernels, Osaka J. Math. 46 (2009), 661-683.
• [2] R. Banuelos, M.M.H. Pang, Stability and approximations of eigenvalues and eigenfunc-tions for the Neumann Laplacian, I, Electron. J. Differential Equations 2008 (2008) 145, 1-13.
• [3] S.A. Buterin, On an inverse spectral problem for a convolution integro-differential op­erator, Resulta Math. 50 (2007), 173-181.
• [4] X. Ding, P. Luo, Finite element approximation of an integro-differential operator, Acta Mathematica Scientia 29B (2009), 1767-1776.
• [5] D. Fortin, Eigenvectors of Toeplitz matrices under higher order three term recurrence and circulant perturbations, Int. J. Pure Appl. Math. 60 (2010) 2, 217-228.
• [6] M.I. Gil', Perturbations of simple eigenvectors of linear operators, Manuscripta Math. 100 (1999), 213-219.
• [7] M.I. Gil', Operator Functions and Localization of Spectra, Lecture Notes in Mathemat­ics, Vol. 1830, Springer-Verlag, Berlin, 2003.
• [8] I.C. Gohberg, M.G. Krein, Introduction to the Theory of Linear Nonselfadjoint Opera­tors, Trans. Mathem. Monographs, Vol. 18, Amer. Math. Soc, Providence, R.I., 1969.
• [9] E. Hunsicker, V. Nistor, J.O. Sofo, Analysis of periodic Schrodinger operators: regularity and approximation of eigenfunctions, J. Math. Phys. 49 (2008) 8, 083501, 21 pp.
• [10] T. Kato, Perturbation Theory for Linear Operators, Springer-Verlag, Berlin, 1980.
• [11] M. Marcus, H. Mine, A Survey of Matrix Theory and Matrix Inequalities, Allyn and Bacon, Boston, 1964.
• [12] F. Nardini, Approximation of Schrodinger eigenvalues and eigenfunctions by canonical perturbation theory: The periodically driven quantum rotator, J. Math. Phys. 30 (1989), 2599-2606.
• [13] M.M.H. Pang, Approximation of ground state eigenvalues and eigenfunctions of Dirich-let Laplacians, Bull. Lond. Math. Soc. 29 (1997), 720-730.
• [14] M.M.H. Pang, Stability and approximations of eigenvalues and eigenfunctions for the Neumann Laplacian, Part 2, J. Math. Anal. Appl. 345 (2008) 1, 485-499.
• [15] M.M.H. Pang, Stability and approximations of eigenvalues and eigenfunctions of the Neumann Laplacian, Part 3, Electron. J. Differential Equations 2011 (2011) 100, 54 pp.
• [16] G. Wang, J. Sun, Approximations of eigenvalues of Sturm-Liouville problems in a given region and corresponding eigenfunctions, Pac. J. Appl. Math. 3 (2011) 1-2, 73-94.