Asymptotic behavior of the weighted trace of Schrodinger equation with operator coefficient given in n-dimensional space
DOI:
https://doi.org/10.22199/S07160917.1999.0001.00007Abstract
We show that an operator formed by Schrodinger differential expression with operator coefficient on separable Hilbert space has a pure discrete spectrum. We also discuss the asymptotic behavior of the weighted trace of this operator.
References
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[2] Boymatov, K. : The asymptotic behavior of thc spectrum of an operator differential equations, Uspehi, Math. Nauk, Vol. 28, No: 4, pp. 207-208, (1973) (Russian).
[3] Eydel'man, S. D. : Parabolic Systems, North-Holland Publishing Company, Amsterdam, (1969).
[4] Gorbaçuk, V. I. and Gorbaçuk, M. L. : Boundary value problems for operator differential equations, Kluwer Academic Publishers Group, London, (1991).
[5] Grinshpun, E. and Rofe-Beketov, F. : Essential self adjointness of some differential operators, in "The Estimates of Spectra of Strum-Liouville Operator" (by M. Otelbaev), Alma-Ata, Nauka, pp. 163-189, (1990) (Russian).
[6] Grinshpun, E. : Locatization Theorems for Equality of Minimal and Maximal Schrodinger-Type operators, J. Functional Analysis 124, pp. 40-60, (1994).
[7] Kirillov, A. A. : Elements of theory representations, Springer Verlag, New York, (1976).
[8] Korenblum, B. I. : General Tauberian theorem for ratio of functions, Dokl. Akad. Nauk SSSR, Vol. 88, pp. 745-748, (1953) (Russian).
[9] Kostjucenko, A. G. and Levitan, B. M. : Asymtotic behavior of the cigenvalues of the Strum-Liouville operator, Funkcional Anal. I Prilozen 1, pp. 86-96, (1967) (Russian).
[10] Kostjucenko, A. G. : The asymtotic behavior of thc spcctral function of self-adjoint elliptic operators, 7. Math. Summer school, Kiev, pp. 42-117, (1968) (Russian).
[11] Levitan, B. M. : On eigenfunction expansions of thc Schrodinger equation in the case of an unbounded potential, Dokl. Akad. Nauk SSSR 103, pp. 191-194, (1955) (Russian).
[12] Levitan, B. M. and Otelbaev, M. : Conditions for selfadjointness of the Schrödinger and Dirac operators, Trans. Moscow Math. Soc. 2, pp. 139-159, (1981).
[13] Mi?naevskiy, G. A. : On Strum-Liouville equation with operator coefficient, Izv. Akad. Nauk SSSR Ser. Mat., 40, No: 1, pp. 152-189, (1976) (Russian).
[14] Reed, M. and Simon, B. : Methods of modern mathematical Physics IV: Analysis of operators, Academic Press, ;.Jcw York, San Francisco, London, (1978).
[15] Solomyak, M. Z. : Asymptotics of the spectrum of the Schrödinger operator with nonregular homogenous potential, Math. USSR Sbornik Vol. 55, No: 1, pp. 19-37, (1986).
[16] Tamura, H. : The asymptotic distribution of eigenvalues of the Laplace operator in an unbounded domain, Nagoya Math. J., Vol. 60, pp. 7-33, (1976).
[17] Yosida, K. : Functional Analysis, Berlin-Göttingen-Heidelberg: Springer Verlag, (1980).
[2] Boymatov, K. : The asymptotic behavior of thc spectrum of an operator differential equations, Uspehi, Math. Nauk, Vol. 28, No: 4, pp. 207-208, (1973) (Russian).
[3] Eydel'man, S. D. : Parabolic Systems, North-Holland Publishing Company, Amsterdam, (1969).
[4] Gorbaçuk, V. I. and Gorbaçuk, M. L. : Boundary value problems for operator differential equations, Kluwer Academic Publishers Group, London, (1991).
[5] Grinshpun, E. and Rofe-Beketov, F. : Essential self adjointness of some differential operators, in "The Estimates of Spectra of Strum-Liouville Operator" (by M. Otelbaev), Alma-Ata, Nauka, pp. 163-189, (1990) (Russian).
[6] Grinshpun, E. : Locatization Theorems for Equality of Minimal and Maximal Schrodinger-Type operators, J. Functional Analysis 124, pp. 40-60, (1994).
[7] Kirillov, A. A. : Elements of theory representations, Springer Verlag, New York, (1976).
[8] Korenblum, B. I. : General Tauberian theorem for ratio of functions, Dokl. Akad. Nauk SSSR, Vol. 88, pp. 745-748, (1953) (Russian).
[9] Kostjucenko, A. G. and Levitan, B. M. : Asymtotic behavior of the cigenvalues of the Strum-Liouville operator, Funkcional Anal. I Prilozen 1, pp. 86-96, (1967) (Russian).
[10] Kostjucenko, A. G. : The asymtotic behavior of thc spcctral function of self-adjoint elliptic operators, 7. Math. Summer school, Kiev, pp. 42-117, (1968) (Russian).
[11] Levitan, B. M. : On eigenfunction expansions of thc Schrodinger equation in the case of an unbounded potential, Dokl. Akad. Nauk SSSR 103, pp. 191-194, (1955) (Russian).
[12] Levitan, B. M. and Otelbaev, M. : Conditions for selfadjointness of the Schrödinger and Dirac operators, Trans. Moscow Math. Soc. 2, pp. 139-159, (1981).
[13] Mi?naevskiy, G. A. : On Strum-Liouville equation with operator coefficient, Izv. Akad. Nauk SSSR Ser. Mat., 40, No: 1, pp. 152-189, (1976) (Russian).
[14] Reed, M. and Simon, B. : Methods of modern mathematical Physics IV: Analysis of operators, Academic Press, ;.Jcw York, San Francisco, London, (1978).
[15] Solomyak, M. Z. : Asymptotics of the spectrum of the Schrödinger operator with nonregular homogenous potential, Math. USSR Sbornik Vol. 55, No: 1, pp. 19-37, (1986).
[16] Tamura, H. : The asymptotic distribution of eigenvalues of the Laplace operator in an unbounded domain, Nagoya Math. J., Vol. 60, pp. 7-33, (1976).
[17] Yosida, K. : Functional Analysis, Berlin-Göttingen-Heidelberg: Springer Verlag, (1980).
Published
2018-04-04
How to Cite
[1]
M. Bayramoğlu and O. Baykal, “Asymptotic behavior of the weighted trace of Schrodinger equation with operator coefficient given in n-dimensional space”, Proyecciones (Antofagasta, On line), vol. 18, no. 1, pp. 91-106, Apr. 2018.
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