Spectral analysis of q-difference equations with spectral singularities

Mathematical and Computer Modelling

Volumn 43, Issue 7-8, 2006, Pages 695-703

  Adivar, Murat ^a   Bohner, Martin ^b  

^a IZMIR UNIVERSITY OF ECONOMICS   (Turkey)

^b MISSOURI UNIVERSITY OF SCIENCE AND TECHNOLOGY   (United States)

Author keywords

Eigenvalue; q difference equation; Spectral analysis; Spectral singularity

Indexed keywords

EIGENVALUES AND EIGENFUNCTIONS; MATHEMATICAL MODELS; PROBLEM SOLVING; SPECTRUM ANALYSIS; THEOREM PROVING;

Q-DIFFERENCE EQUATIONS; SPECTRAL SINGULARITY;

DIFFERENCE EQUATIONS;

EID: 33645018710     PISSN: 08957177     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.mcm.2005.04.014     Document Type: Article

References (21)

1. E. Bairamov, Ö. Çakar, and A.O. Çelebi Quadratic pencil of Schrödinger operators with spectral singularities: Discrete spectrum and principal functions J. Math. Anal. Appl. 216 1 1997 303 320
2. E. Bairamov, Ö. Cakar, and C. Yanik Spectral singularities of the Klein-Gordon s -wave equation Indian J. Pure Appl. Math. 32 6 2001 851 857
3. A.M. Krall, E. Bairamov, and Ö. Çakar Spectrum and spectral singularities of a quadratic pencil of a Schrödinger operator with a general boundary condition J. Differential Equations 151 2 1999 252 267
4. V.E. Lyance A differential operator with spectral singularities I, II Amer. Math. Soc. Transl. 60 2 1967 185-225, 227-283
5. M.A. Naǐmark Investigation of the spectrum and the expansion in eigenfunctions of a non-selfadjoint differential operator of the second order on a semi-axis Amer. Math. Soc. Transl. Ser. 2 16 1960 103 193
6. M.A. Naǐmark Linear Differential Operators. Part II: Linear Differential Operators in Hilbert Space (With additional material by the author, and a supplement by V. È. Ljance. Translated from the Russian by E. R. Dawson. English translation edited by W. N. Everitt) 1968 Frederick Ungar Publishing Co. New York
7. M. Adivar, and E. Bairamov Spectral properties of non-selfadjoint difference operators J. Math. Anal. Appl. 261 2 2001 461 478
8. E. Bairamov, Ö. Çakar, and A.M. Krall Non-selfadjoint difference operators and Jacobi matrices with spectral singularities Math. Nachr. 229 2001 5 14
9. E. Bairamov, and A.O. Çelebi Spectrum and spectral expansion for the non-selfadjoint discrete Dirac operators Quart. J. Math. Oxford Ser. 2 50 200 1999 371 384
10. A.M. Krall, E. Bairamov, and Ö. Çakar Spectral analysis of non-selfadjoint discrete Schrödinger operators with spectral singularities Math. Nachr. 231 2001 89 104
11. R.P. Agarwal Difference Equations and Inequalities Monographs and Textbooks in Pure and Applied Mathematics vol. 228 2000 Marcel Dekker Inc. New York
12. R.P. Agarwal, and P.J.Y. Wong Advanced Topics in Difference Equations Mathematics and its Applications vol. 404 1997 Kluwer Academic Publishers Group Dordrecht
13. V. Kac, and P. Cheung Quantum calculus Universitext 2002 Springer-Verlag New York
14. M. Bohner, and A. Peterson Dynamic Equations on Time Scales 2001 Birkhäuser Boston Inc. Boston, MA
15. M. Bohner, and A. Peterson Advances in Dynamic Equations on Time Scales 2003 Birkhäuser Boston Inc. Boston, MA
16. C. Berg, and A. Ruffing Generalized q -Hermite polynomials Comm. Math. Phys. 223 1 2001 29 46
17. J.-P. Bézivin Sur les équations fonctionnelles aux q -différences Aequationes Math. 43 2-3 1992 159 176
18. W.J. Trijtzinsky Analytic theory of linear q -difference equations Acta Math. 61 1933 1 38
19. C. Zhang Sur la sommabilité des séries entières solutions formelles d'une équation aux q -différences. I C. R. Acad. Sci. Paris Sér. I Math. 327 4 1998 349 352
20. I.M. Glazman, Direct methods of qualitative spectral analysis of singular differential operators, in: Israel Program for Scientific Translations, Jerusalem, 1965, 1966. Translated from the Russian by the IPST staff
21. E.P. Dolzhenko Boundary value uniqueness theorems for analytic functions Math. Notes 26 1979 437 442