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The Regularized Trace of Two Terms Differential Operator in the Space H1 = L2 (0,𝝅;𝑯).

Year 2019, Volume: 9 Issue: 3, 1594 - 1605, 01.09.2019

Abstract

The main purpose of this present paper is to derive a trace formula for a selfadjoint differential operator which is defined in Hilbert space.

References

  • Adıguzelov EE, (1976). About the trace of the difference of two Sturm-Liouville operators with the operator coefficient. Iz. An Az. SSR, Seriya Fiz-Tekn. i Mat. Nauk, 5: 20-24.
  • Adiguzelov E, Baksi O, (2004). On the regularized trace of the differential operator equation given in a finite interval. Journal of Engineering and Natural Science, Sigma, 1: 47-55.
  • Adiguzelov E, Sezer Y, (2011). The second regularized trace of a self adjoint differential operator given in a finite interval with bounded operator coefficient. Mathematical and Computer Modeling, 53: 553-565.
  • Baksi O, Karayel S, Sezer Y, (2017). Second regularized trace of a differential operator with second order unbounded operator coefficient given in a finite interval. Operators and Matrices, 11(3): 735-747.
  • Bayramoglu M, (1986). The trace formula for the abstract Sturm-Liouville equation with continuous spectrum. Akad. Nauk Azerb. SSR., Inst. Fiz., Baku, Preprint 6, 34.
  • Chalilova RZ, (1976). On arranging Sturm-Liouville operator equation’s trace. Funks, Analiz, Teoriya funksiy i ik pril-Mahaçkala, 3 (part I), 154-161.
  • Dikiy LA, (1953). About of a formula of Gelfand-Levitan. Uspekhi Matematicheskikh Nauk, 8: 119-123.
  • Dikiy LA, (1955). The Zeta Function of an ordinary differential equation on a finite interval. IZV. Akad. Nauk. SSSR, 19(4): 187-200.
  • Faddeev LD, (1957). On the expression for the trace of the difference of two singular differential operators of the Sturm Liouville Type. Doklady Akademii Nauk SSSR, 115(5): 878-881.
  • Fulton CT, Pruess SA, (1994). Eigenvalue and eigenfunction asymptotics for regular Sturm-Liouville problems. Journal of Mathematical Analysis and Applications, 188(1): 297-340.
  • Gasymov MG, (1963). On the sum of differences of eigenvalues of two self adjoint operators. Doklady Akademii Nauk SSSR, 150(6): 1202-1205.
  • Gelfand IM, Levitan BM, (1953). On a formula for eigenvalues of a differential operator of second order. Doklady Akademii Nauk SSSR, 88: 593-596.
  • Gelfand IM, (1956). On the identities for eigenvalues of differential operator of second order. Uspekhi Mat. Nauk (N.S.), 11(1): 191-198.
  • Gohberg IC, Krein MG, (1969). Introduction to the theory of linear non-self adjoint operators. Translation of Mathematical Monographs, Vol. 18 (AMS, Providence, RI,)
  • Gorbachuk, VI, (1975). On the asymptotic behavior of the eigenvalues of boundary value problems for differential equations in a space of vector valued functions. Ukr. Matem. J., 27(5): 657-664.
  • Halberg CJ, Kramer VA, (1960). A generalization of the trace concept. Duke Mathematical Journal, 27(4): 607-618.
  • Karayel S, Sezer Y, (2015). The regularized trace formula for a fourth-order differential operator given in a finite interval. Journal of Inequalities and Applications, 316: 1-10.
  • Krein MG, (1953). The trace formula in the perturbation theory. Matem., 56.33(153): 597-626.
  • Levitan BM, Sargsyan IS, 1991. Sturm-Liouville and Dirac Operators. Kluwer Academic Publishers, Dordrecht, Boston, London.
  • Levitan BM, (1964). Calculation of the regularized trace for the Sturm Liouville Operator. Uspekhi Mat. Nauk, 19(1): 161-165.
  • Lidskiy VB, Sadovniciy VA, (1967). The regularized sum of roots of complete functions belonging to a class. Funks. analiz i pril., 1: 52-59.
  • Maksudov FG, Baiamoglu M, Adıguzelov EE, (1984). On regularized trace of Sturm-Liouville operator on a finite interval with the unbounded operator coefficient. Doklady Akademii Nauk SSSR, 30: 169-173.
  • Sadovnichii VA, (1966). On the trace of the difference of two ordinary differential operators of higher order. Differ. Uravn., 2(12): 1611-1624.
  • Sadovnichii VA, Podol’skii VE, (2009). Traces of Differential Operators. Differential Equations, 45(4): 477-493.
  • Sen E, Bayramov A, Orucoglu K, (2015). The regularized trace formula for a differential operator with unbounded operator coefficient. Advanced Studies in Contemporary Mathematics, 25: 583-591.
  • Sen E, Bayramov A, Orucoglu K, (2016). Regularized trace formula for higher order differential operators with unbounded coefficient. Electronic Journal of Differential Equations, 2016: 1-12.
  • Sen E, (2017). A regularized trace formula and oscillation of eigenfunctions of a Sturm-Liouville operator with retarded argument at 2 points of discontinuity. Mathematical Methods in the Applied Sciences, 40: 7051-7061.
  • Yang C-F, (2013). New trace formula for the matrix Sturm-Liouville equation with eigen parameter dependent boundary conditions. Turk. J. Math., 37: 278-285.

H1 = L2 (0,π;H) Uzayında İki Terimli Diferansiyel Operatörün Düzenli İzi

Year 2019, Volume: 9 Issue: 3, 1594 - 1605, 01.09.2019

Abstract

Mevcut çalışmanın esas amacı Hilbert uzayında tanımlanmış bir kendine-eş diferansiyel operatör için bir iz formülü çıkarmaktır.

References

  • Adıguzelov EE, (1976). About the trace of the difference of two Sturm-Liouville operators with the operator coefficient. Iz. An Az. SSR, Seriya Fiz-Tekn. i Mat. Nauk, 5: 20-24.
  • Adiguzelov E, Baksi O, (2004). On the regularized trace of the differential operator equation given in a finite interval. Journal of Engineering and Natural Science, Sigma, 1: 47-55.
  • Adiguzelov E, Sezer Y, (2011). The second regularized trace of a self adjoint differential operator given in a finite interval with bounded operator coefficient. Mathematical and Computer Modeling, 53: 553-565.
  • Baksi O, Karayel S, Sezer Y, (2017). Second regularized trace of a differential operator with second order unbounded operator coefficient given in a finite interval. Operators and Matrices, 11(3): 735-747.
  • Bayramoglu M, (1986). The trace formula for the abstract Sturm-Liouville equation with continuous spectrum. Akad. Nauk Azerb. SSR., Inst. Fiz., Baku, Preprint 6, 34.
  • Chalilova RZ, (1976). On arranging Sturm-Liouville operator equation’s trace. Funks, Analiz, Teoriya funksiy i ik pril-Mahaçkala, 3 (part I), 154-161.
  • Dikiy LA, (1953). About of a formula of Gelfand-Levitan. Uspekhi Matematicheskikh Nauk, 8: 119-123.
  • Dikiy LA, (1955). The Zeta Function of an ordinary differential equation on a finite interval. IZV. Akad. Nauk. SSSR, 19(4): 187-200.
  • Faddeev LD, (1957). On the expression for the trace of the difference of two singular differential operators of the Sturm Liouville Type. Doklady Akademii Nauk SSSR, 115(5): 878-881.
  • Fulton CT, Pruess SA, (1994). Eigenvalue and eigenfunction asymptotics for regular Sturm-Liouville problems. Journal of Mathematical Analysis and Applications, 188(1): 297-340.
  • Gasymov MG, (1963). On the sum of differences of eigenvalues of two self adjoint operators. Doklady Akademii Nauk SSSR, 150(6): 1202-1205.
  • Gelfand IM, Levitan BM, (1953). On a formula for eigenvalues of a differential operator of second order. Doklady Akademii Nauk SSSR, 88: 593-596.
  • Gelfand IM, (1956). On the identities for eigenvalues of differential operator of second order. Uspekhi Mat. Nauk (N.S.), 11(1): 191-198.
  • Gohberg IC, Krein MG, (1969). Introduction to the theory of linear non-self adjoint operators. Translation of Mathematical Monographs, Vol. 18 (AMS, Providence, RI,)
  • Gorbachuk, VI, (1975). On the asymptotic behavior of the eigenvalues of boundary value problems for differential equations in a space of vector valued functions. Ukr. Matem. J., 27(5): 657-664.
  • Halberg CJ, Kramer VA, (1960). A generalization of the trace concept. Duke Mathematical Journal, 27(4): 607-618.
  • Karayel S, Sezer Y, (2015). The regularized trace formula for a fourth-order differential operator given in a finite interval. Journal of Inequalities and Applications, 316: 1-10.
  • Krein MG, (1953). The trace formula in the perturbation theory. Matem., 56.33(153): 597-626.
  • Levitan BM, Sargsyan IS, 1991. Sturm-Liouville and Dirac Operators. Kluwer Academic Publishers, Dordrecht, Boston, London.
  • Levitan BM, (1964). Calculation of the regularized trace for the Sturm Liouville Operator. Uspekhi Mat. Nauk, 19(1): 161-165.
  • Lidskiy VB, Sadovniciy VA, (1967). The regularized sum of roots of complete functions belonging to a class. Funks. analiz i pril., 1: 52-59.
  • Maksudov FG, Baiamoglu M, Adıguzelov EE, (1984). On regularized trace of Sturm-Liouville operator on a finite interval with the unbounded operator coefficient. Doklady Akademii Nauk SSSR, 30: 169-173.
  • Sadovnichii VA, (1966). On the trace of the difference of two ordinary differential operators of higher order. Differ. Uravn., 2(12): 1611-1624.
  • Sadovnichii VA, Podol’skii VE, (2009). Traces of Differential Operators. Differential Equations, 45(4): 477-493.
  • Sen E, Bayramov A, Orucoglu K, (2015). The regularized trace formula for a differential operator with unbounded operator coefficient. Advanced Studies in Contemporary Mathematics, 25: 583-591.
  • Sen E, Bayramov A, Orucoglu K, (2016). Regularized trace formula for higher order differential operators with unbounded coefficient. Electronic Journal of Differential Equations, 2016: 1-12.
  • Sen E, (2017). A regularized trace formula and oscillation of eigenfunctions of a Sturm-Liouville operator with retarded argument at 2 points of discontinuity. Mathematical Methods in the Applied Sciences, 40: 7051-7061.
  • Yang C-F, (2013). New trace formula for the matrix Sturm-Liouville equation with eigen parameter dependent boundary conditions. Turk. J. Math., 37: 278-285.
There are 28 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Matematik / Mathematics
Authors

Özlem Bakşi 0000-0002-2423-8676

Publication Date September 1, 2019
Submission Date October 15, 2018
Acceptance Date March 17, 2019
Published in Issue Year 2019 Volume: 9 Issue: 3

Cite

APA Bakşi, Ö. (2019). The Regularized Trace of Two Terms Differential Operator in the Space H1 = L2 (0,𝝅;𝑯). Journal of the Institute of Science and Technology, 9(3), 1594-1605.
AMA Bakşi Ö. The Regularized Trace of Two Terms Differential Operator in the Space H1 = L2 (0,𝝅;𝑯). J. Inst. Sci. and Tech. September 2019;9(3):1594-1605.
Chicago Bakşi, Özlem. “𝑯)”. Journal of the Institute of Science and Technology 9, no. 3 (September 2019): 1594-1605.
EndNote Bakşi Ö (September 1, 2019) The Regularized Trace of Two Terms Differential Operator in the Space H1 = L2 (0,𝝅;𝑯). Journal of the Institute of Science and Technology 9 3 1594–1605.
IEEE Ö. Bakşi, “𝑯)”., J. Inst. Sci. and Tech., vol. 9, no. 3, pp. 1594–1605, 2019.
ISNAD Bakşi, Özlem. “𝑯)”. Journal of the Institute of Science and Technology 9/3 (September 2019), 1594-1605.
JAMA Bakşi Ö. The Regularized Trace of Two Terms Differential Operator in the Space H1 = L2 (0,𝝅;𝑯). J. Inst. Sci. and Tech. 2019;9:1594–1605.
MLA Bakşi, Özlem. “𝑯)”. Journal of the Institute of Science and Technology, vol. 9, no. 3, 2019, pp. 1594-05.
Vancouver Bakşi Ö. The Regularized Trace of Two Terms Differential Operator in the Space H1 = L2 (0,𝝅;𝑯). J. Inst. Sci. and Tech. 2019;9(3):1594-605.