Nonstandard Sturm-Liouville difference operator, II

V.E. Lyantse; Yu.M. Yavorsky

This article extends the investigation with the same title printed in the previous volume of ``Mat. studii''. We consider the spectrum and spectral expansion of a nonstandard ordinary singular Sturm-Liouville operator $L$ in finite differences. The resolvent of $L$ is considered and its norm is estimated.

1. M.A. Naimark Investigation of the spectrum and expansion in eigenfunctions of a non-selfadjoint differential operator of the 2nd order on the half-axis // Trudy Moskow. Mat. Obshch. V. 3 p.181–270–1954 (in Russian)

2. V.E. Lyantse The non-selfadjoint differential operator of the second order on the half-axis. Appendix 2M.A. Naimark, Linear differential operators, part 2 , F. Ungar Publishing CO, New York, p. 292–331, 1968

3. V.A. Marchenko Eigenfunction expansions for non-selfadjoint singular differential operators of the second order// Matem. Sb. V. 52 p. 739–788– 1960 (in Russian)

4. N. Dunford and J. Schwartz Linear operators, Part 3. Spectral operators, Wiley-Interscience ,addr New York-London-Sydney-Toronto–1971

5. V.E. Lyantse On the differential operator with the spectral singularities// Mat. Sb. V. 64№4–1964p. 521–561, 65. (1964), no. 1, 47–103 (in Russian)

6. V.E. Lyantse Expansion in eigenfunction // Rev. Roum. Math. Pures et Appl. V. 11№8–1966p. 921–950, 11. (1966), no. 10, 1187–1224

7. V.E. Lyantse Perturbation of continuous spectrum // Dokl. AN SSSR V. 187p. 514–517–1969 Russian

8. V.A. Blashchak On the second–order differential operator on the whole axis with the spectral singularities// Dokl. AN UkrSSR V. 1p. 38–41–1966 (in Russian)

9. E. Nelson Internal Set Theory// Bull. Amer. Math. Soc. V. 83p. 1165–1198–1977

10. E. Nelson Radically Elementary Probability Theory , Princeton Univercity Press–1987

11. F. Diener Cours d'analyse non standard, Offices des Publications Universitaires,addr Alger–1983

12. R. Lutz, M. Goze Non standard analysis: a practical guide with applications (Lect. Notes in Math. V. 881) , Springer Verlag, Berlin et New Jork - 1981

13. P. Cartier Perturbations singulièrs et analyse non standard// Astérisque, Séminaire Bourbaki V. 92–93–1982

14. G. Reeb Mathématique non standard (essai de vulgarisation)// Bull. AP–MEP V. 328p. 258–273 - 1981

15. W. Lyantse Spectrum and resolvent of finite difference operator// Ukr. Math. J. V. 20№ 4 - 1968p. 489-503 21. (1969), no. 4, 461–474

16. V. Lyantse, Yu. Yavorsky Nonstandard Sturm-Liouville difference operator // Mat. studii V. 10 - 1998 № 1 p. 58-64

	Nonstandard Sturm-Liouville difference operator, II
Author	V.E. Lyantse, Yu.M. Yavorsky wlanc@litech.lviv.ua Department of Mathematics,Lviv State
Abstract	This article extends the investigation with the same title printed in the previous volume of ``Mat. studii''. We consider the spectrum and spectral expansion of a nonstandard ordinary singular Sturm-Liouville operator $L$ in finite differences. The resolvent of $L$ is considered and its norm is estimated.
Keywords	nonstandard Sturm-Liouville operator, ordinary singular differential operator, finite differences, spectrum, spectral expansion
DOI	doi:10.30970/ms.11.1.71-82
Reference	1. M.A. Naimark Investigation of the spectrum and expansion in eigenfunctions of a non-selfadjoint differential operator of the 2nd order on the half-axis // Trudy Moskow. Mat. Obshch. V. 3 p.181–270–1954 (in Russian) 2. V.E. Lyantse The non-selfadjoint differential operator of the second order on the half-axis. Appendix 2M.A. Naimark, Linear differential operators, part 2 , F. Ungar Publishing CO, New York, p. 292–331, 1968 3. V.A. Marchenko Eigenfunction expansions for non-selfadjoint singular differential operators of the second order// Matem. Sb. V. 52 p. 739–788– 1960 (in Russian) 4. N. Dunford and J. Schwartz Linear operators, Part 3. Spectral operators, Wiley-Interscience ,addr New York-London-Sydney-Toronto–1971 5. V.E. Lyantse On the differential operator with the spectral singularities// Mat. Sb. V. 64№4–1964p. 521–561, 65. (1964), no. 1, 47–103 (in Russian) 6. V.E. Lyantse Expansion in eigenfunction // Rev. Roum. Math. Pures et Appl. V. 11№8–1966p. 921–950, 11. (1966), no. 10, 1187–1224 7. V.E. Lyantse Perturbation of continuous spectrum // Dokl. AN SSSR V. 187p. 514–517–1969 Russian 8. V.A. Blashchak On the second–order differential operator on the whole axis with the spectral singularities// Dokl. AN UkrSSR V. 1p. 38–41–1966 (in Russian) 9. E. Nelson Internal Set Theory// Bull. Amer. Math. Soc. V. 83p. 1165–1198–1977 10. E. Nelson Radically Elementary Probability Theory , Princeton Univercity Press–1987 11. F. Diener Cours d'analyse non standard, Offices des Publications Universitaires,addr Alger–1983 12. R. Lutz, M. Goze Non standard analysis: a practical guide with applications (Lect. Notes in Math. V. 881) , Springer Verlag, Berlin et New Jork - 1981 13. P. Cartier Perturbations singulièrs et analyse non standard// Astérisque, Séminaire Bourbaki V. 92–93–1982 14. G. Reeb Mathématique non standard (essai de vulgarisation)// Bull. AP–MEP V. 328p. 258–273 - 1981 15. W. Lyantse Spectrum and resolvent of finite difference operator// Ukr. Math. J. V. 20№ 4 - 1968p. 489-503 21. (1969), no. 4, 461–474 16. V. Lyantse, Yu. Yavorsky Nonstandard Sturm-Liouville difference operator // Mat. studii V. 10 - 1998 № 1 p. 58-64
Pages	71-82
Volume	11
Issue	1
Year	1999
Journal	Matematychni Studii
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