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2018 | 72 | 1 |

Tytuł artykułu

Spectral analysis of singular Sturm-Liouville operators on time scales

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Warianty tytułu

Języki publikacji

EN

Abstrakty

EN
In this paper, we consider properties of the spectrum of a Sturm-Liouvilleoperator on time scales. We will prove that the regular symmetricSturm-Liouville operator is semi-bounded from below. We will also give someconditions for the self-adjoint operator associated with the singularSturm-Liouville expression to have a discrete spectrum. Finally, we willinvestigate the continuous spectrum of this operator.

Rocznik

Tom

72

Numer

1

Opis fizyczny

Daty

wydano
2018
online
2018-06-25

Bibliografia

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  • Bohner, M., Peterson, A., Dynamic Equations on Time Scales, Birkhauser, Boston, 2001.
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  • Guseinov, G. Sh., An expansion theorem for a Sturm-Liouville operator on semiunbounded time scales, Adv. Dyn. Syst. Appl. 3 (1) (2008), 147-160.
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  • Molchanov, A. M., Conditions for the discreteness of the spectrum of self-adjoint second-order differential equations, Trudy Moskov. Mat. Obs. 2 (1953), 169-200 (Russian).
  • Naimark, M. A., Linear Differential Operators, 2nd edition., Nauka, Moscow, 1969, English transl. of 1st edition, Frederick Ungar Publishing Co., New York, 1969.
  • Rollins, L. W., Criteria for discrete spectrum of singular self-adjoint differential operators, Proc. Amer. Math. Soc. 34 (1972), 195-200.
  • Rynne, B. P., \(L^2\) spaces and boundary value problems on time-scales, J. Math. Anal. Appl. 328 (2007), 1217-1236.
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Bibliografia

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bwmeta1.element.ojs-doi-10_17951_a_2018_72_1_1-11
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