Regularized trace of sturm-liouville equation with singilarity on a bounded segment

İlyas Haşimoğlu

doi:10.1501/Commua1_0000000673

Regularized trace of sturm-liouville equation with singilarity on a bounded segment

Year 2012, Volume: 61 Issue: 1, 1 - 9, 01.02.2012

İlyas Haşimoğlu

https://doi.org/10.1501/Commua1_0000000673

Keywords

Regularized trace, Sturm-Liouville operators

References

I.M.Gelfand, B.M.Levitan, On the simple identity for the eigenvalues of second order diğer- ential operator. Doklady Akademii Nauk SSSR, 88(1953) 593-596
M.G.Gasimov , The sum of diğerence of eigenvalues of two singular Sturm-Liouville operators. Doklady Akademii Nauk SSSR, 151(1963) 1014-1017
L.A.Dikiy, On the Gelfand-Levitan formula. Uspekhi Mat. Nauk, 7(1953) 119-123
L.A.Dikiy, Zeta function of ordinary diğerential equation on the segment. Izvestiya Akademii Nauk SSSR, ser. Matematika, 19(1955) 187-200
V.A.Sadovnichiy, The trace of ordinary diğerential operators. Mat. Zametki 1(1967) 179-188
V.A.Sadovnichiy, The identity of eigenvalues of Dirac system and some other systems of high order. Vestnik MGU 3(1967) 37-47
V.A.Sadovnichiy, Some identities for the eigenvalues of singular diğerential operators. Re- lations for the zeros of the Bessel function. Vestnik MGU , ser. Matem. Mechan. 3(1971) 86
V.A.Sadovnichiy, Zeta function and eigenvalues of diğerential operators. Diğerensiyalniye uravneniya 10(1974) 1276-1285
V.A.Sadovnichiy, The trace of high order diğerential operators. Diğerensialniye uravneniya (1996) , 1611-1624
F.G.Maksudov, M.Bairamoglu, A.A.Adigozelov, On the regularized trace on the segment of Sturm-Liouville operator with unbounded operator coe¢ cients. Doklady Akademii Nauk SSSR, 277(1984) 795-799
V.A.Lyubishkin, Formulae of Gelfand-Levitan and Crayn. Math. Sbornik, 182(1991) 1786
V.A.Lyubishkin, V.E. Podolskiy, On the summarizing of regularized traces of diğerential operators. Mat. Zametki, 54(1993), 33-38
V.G. Papanicolaou, Trace formulas and the behavior of large eigenvalues. SIAM J. Math.Anal. (1995) 218-237
F.Gesztesy, H.Holden, B.Simon and Z.Zhao, Trace formulae and inverse spectral theory for Schroedinger operators. Bull. Amer. Math. Soc. 29(1993) 250-255
V.A.Vinokurov, V.A.Sadovnichiy, Asymptote of eigenvalues and eigenfunctions and trace formula for the potential contains 448 function. Doklady Akademii Nauk SSSR, 376(2001)
A.M.Savchuk, A.A.Shkalikov, Trace formula for the Sturm-Liouville operator with singular potential. Mat. Zametki, 69(2001) 427-442
G.N.Watson, A tretise on the theory of Bessel functions. Cambridge University Press, Cam- bridge, 1992
Current address : Ilyas Ha¸simo¼glu; Karabuk University, Karabuk, TURKEY and Institute of Mathematics, Academy of Sciences of Azerbaijan, Baku, Azerbaijan E-mail address : ilyas_hashimov@yahoo.com URL: http://communications.science.ankara.edu.tr/index.php?series=A1

Year 2012, Volume: 61 Issue: 1, 1 - 9, 01.02.2012

İlyas Haşimoğlu

https://doi.org/10.1501/Commua1_0000000673

References

I.M.Gelfand, B.M.Levitan, On the simple identity for the eigenvalues of second order diğer- ential operator. Doklady Akademii Nauk SSSR, 88(1953) 593-596
M.G.Gasimov , The sum of diğerence of eigenvalues of two singular Sturm-Liouville operators. Doklady Akademii Nauk SSSR, 151(1963) 1014-1017
L.A.Dikiy, On the Gelfand-Levitan formula. Uspekhi Mat. Nauk, 7(1953) 119-123
L.A.Dikiy, Zeta function of ordinary diğerential equation on the segment. Izvestiya Akademii Nauk SSSR, ser. Matematika, 19(1955) 187-200
V.A.Sadovnichiy, The trace of ordinary diğerential operators. Mat. Zametki 1(1967) 179-188
V.A.Sadovnichiy, The identity of eigenvalues of Dirac system and some other systems of high order. Vestnik MGU 3(1967) 37-47
V.A.Sadovnichiy, Some identities for the eigenvalues of singular diğerential operators. Re- lations for the zeros of the Bessel function. Vestnik MGU , ser. Matem. Mechan. 3(1971) 86
V.A.Sadovnichiy, Zeta function and eigenvalues of diğerential operators. Diğerensiyalniye uravneniya 10(1974) 1276-1285
V.A.Sadovnichiy, The trace of high order diğerential operators. Diğerensialniye uravneniya (1996) , 1611-1624
F.G.Maksudov, M.Bairamoglu, A.A.Adigozelov, On the regularized trace on the segment of Sturm-Liouville operator with unbounded operator coe¢ cients. Doklady Akademii Nauk SSSR, 277(1984) 795-799
V.A.Lyubishkin, Formulae of Gelfand-Levitan and Crayn. Math. Sbornik, 182(1991) 1786
V.A.Lyubishkin, V.E. Podolskiy, On the summarizing of regularized traces of diğerential operators. Mat. Zametki, 54(1993), 33-38
V.G. Papanicolaou, Trace formulas and the behavior of large eigenvalues. SIAM J. Math.Anal. (1995) 218-237
F.Gesztesy, H.Holden, B.Simon and Z.Zhao, Trace formulae and inverse spectral theory for Schroedinger operators. Bull. Amer. Math. Soc. 29(1993) 250-255
V.A.Vinokurov, V.A.Sadovnichiy, Asymptote of eigenvalues and eigenfunctions and trace formula for the potential contains 448 function. Doklady Akademii Nauk SSSR, 376(2001)
A.M.Savchuk, A.A.Shkalikov, Trace formula for the Sturm-Liouville operator with singular potential. Mat. Zametki, 69(2001) 427-442
G.N.Watson, A tretise on the theory of Bessel functions. Cambridge University Press, Cam- bridge, 1992
Current address : Ilyas Ha¸simo¼glu; Karabuk University, Karabuk, TURKEY and Institute of Mathematics, Academy of Sciences of Azerbaijan, Baku, Azerbaijan E-mail address : ilyas_hashimov@yahoo.com URL: http://communications.science.ankara.edu.tr/index.php?series=A1

There are 18 citations in total.

Details

Primary Language	English
Journal Section	Research Articles
Authors	İlyas Haşimoğlu This is me
Publication Date	February 1, 2012
Published in Issue	Year 2012 Volume: 61 Issue: 1

Cite

APA	Haşimoğlu, İ. (2012). Regularized trace of sturm-liouville equation with singilarity on a bounded segment. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 61(1), 1-9. https://doi.org/10.1501/Commua1_0000000673
AMA	Haşimoğlu İ. Regularized trace of sturm-liouville equation with singilarity on a bounded segment. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. February 2012;61(1):1-9. doi:10.1501/Commua1_0000000673
Chicago	Haşimoğlu, İlyas. “Regularized Trace of Sturm-Liouville Equation With Singilarity on a Bounded Segment”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 61, no. 1 (February 2012): 1-9. https://doi.org/10.1501/Commua1_0000000673.
EndNote	Haşimoğlu İ (February 1, 2012) Regularized trace of sturm-liouville equation with singilarity on a bounded segment. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 61 1 1–9.
IEEE	İ. Haşimoğlu, “Regularized trace of sturm-liouville equation with singilarity on a bounded segment”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 61, no. 1, pp. 1–9, 2012, doi: 10.1501/Commua1_0000000673.
ISNAD	Haşimoğlu, İlyas. “Regularized Trace of Sturm-Liouville Equation With Singilarity on a Bounded Segment”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 61/1 (February 2012), 1-9. https://doi.org/10.1501/Commua1_0000000673.
JAMA	Haşimoğlu İ. Regularized trace of sturm-liouville equation with singilarity on a bounded segment. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2012;61:1–9.
MLA	Haşimoğlu, İlyas. “Regularized Trace of Sturm-Liouville Equation With Singilarity on a Bounded Segment”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 61, no. 1, 2012, pp. 1-9, doi:10.1501/Commua1_0000000673.
Vancouver	Haşimoğlu İ. Regularized trace of sturm-liouville equation with singilarity on a bounded segment. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2012;61(1):1-9.