Voir la notice de l'article provenant de la source Math-Net.Ru
@article{VVGUM_2018_21_2_a1, author = {S. I. Mitrokhin}, title = {About the spectral properties of the family of the differential operator of even order with summable potential}, journal = {Matemati\v{c}eska\^a fizika i kompʹ\^uternoe modelirovanie}, pages = {13--26}, publisher = {mathdoc}, volume = {21}, number = {2}, year = {2018}, language = {ru}, url = {http://geodesic.mathdoc.fr/item/VVGUM_2018_21_2_a1/} }
TY - JOUR AU - S. I. Mitrokhin TI - About the spectral properties of the family of the differential operator of even order with summable potential JO - Matematičeskaâ fizika i kompʹûternoe modelirovanie PY - 2018 SP - 13 EP - 26 VL - 21 IS - 2 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/VVGUM_2018_21_2_a1/ LA - ru ID - VVGUM_2018_21_2_a1 ER -
%0 Journal Article %A S. I. Mitrokhin %T About the spectral properties of the family of the differential operator of even order with summable potential %J Matematičeskaâ fizika i kompʹûternoe modelirovanie %D 2018 %P 13-26 %V 21 %N 2 %I mathdoc %U http://geodesic.mathdoc.fr/item/VVGUM_2018_21_2_a1/ %G ru %F VVGUM_2018_21_2_a1
S. I. Mitrokhin. About the spectral properties of the family of the differential operator of even order with summable potential. Matematičeskaâ fizika i kompʹûternoe modelirovanie, Tome 21 (2018) no. 2, pp. 13-26. http://geodesic.mathdoc.fr/item/VVGUM_2018_21_2_a1/
[1] R. Bellman, K. L. Cooke, Differential-Difference Equations, Mir Publ., Moscow, 1967, 548 pp.
[2] V. A. Vinokurov, V. A. Sadovnichiy, “Asymptotics of Any Order for Eigenvalues and Eigenfunctions of the Boundary Value of Sturm-Liouville Problem on a Segment with Summable Potential”, Differential Equations, 34:10 (1998), 1423–1426 | MR | Zbl
[3] V. A. Ilyin, “About the Convergence of Eigenfunction Expansions at Discontinuity Points of Differential Operator’s Coefficients”, Mathematical Notes, 22:5 (1977), 698–723
[4] V. B. Lidskiy, V. A. Sadovnichiy, “Asymptotic Formulas for the Roots of One Class of Entire Functions”, Mathematical Collection, 75:4, no. 117 (1968), 558–566 | MR | Zbl
[5] D. Sh. Lundina, “Exact Relationship between the AsymptoticExpansions of the Eigenvalues of Boundary Value Problems of the Sturm-Liouville Problem and the Smoothness ofPotential”, The Theory of Functions, Functional Analysisand Their Applications, 1982, no. 37, 74–101 | MR | Zbl
[6] V. A. Marchenko, Sturm–Liouville Operators and TheirApplications, Naukova Dumka Publ., Kiev, 1977, 329 pp. | MR
[7] S. I. Mitrokhin, “Asymptotics of the Eigenvalues of the Differential Operator of the Fourth Orderwith Summable Coefficients”, Vestnik Moskovskogo universiteta. Seriya: Matematika, mehanika, 2009, no. 3, 14–17 | MR | Zbl
[8] “About Some Spectral Properties of Differential Operators of the Second Order withDiscontinuous Weight Function”, Reports of the Russian Academy of Sciences, 356:1 (1997), 13–15 | MR | Zbl
[9] S. I. Mitrokhin, “About “Splitting” in the Main Multiple Eigenvalues of Boundary Value Problems”, Proceedings of the Universities. Series: Mathematics, 3:418 (1997), 38–43 | MR | Zbl
[10] S. I. Mitrokhin, “About Spectral Properties of Differential Operators of Odd Order with Summable Potential”, Differential Equations, 47:2 (2011), 1808–1811 | MR | Zbl
[11] S. I. Mitrokhin, “About Spectral Properties of One Differential Operator withSummable Coefficients with a Retarded Argument”, Ufa Mathematical Journal, 3:4 (2011), 95–115 | MR | Zbl
[12] S. I. Mitrokhin, “About Formulas of Regularized Traces for Differential Operators of the Second Orderwith Discontinuous Coefficients”, Vestnik Moskovskogo universiteta. Seriya: Matematika, mekhanika, 1986, no. 6, 3–6 | MR
[13] S. I. Mitrokhin, “About the Formulas of Traces for a Boundary Value Problem with Functional DifferentialEquation with a Discontinuous Coefficient”, Differential Equations, 22:6 (1986), 927–931 | MR | Zbl
[14] M. A. Naimark, Linear Differential Operators, Nauka Publ., Moscow, 1969, 528 pp.
[15] V. A. Sadovnichiy, V. A. Lyubishkin, Yu. Belabassi, “About Regularized Sums of the Roots of the Entire Function of One Class”, Reports of the Academy of Sciences of the USSR, 254:6 (1980), 1346–1348 | MR
[16] V. A. Sadovnichiy, “On the Traces of Ordinary Differential Operators of Higher Orders”, Mathematical Collection, 72:2 (1967), 293–317 | Zbl
[17] H. P. W. Gottlieb, “Iso-spectral operators: some model examples with discontinuous coefficients”, Journal of Math. Anal. and Appl., 132 (1988), 123–137 | DOI | MR | Zbl
[18] O. H. Hald, “Discontinuous inverse eigenvalue problems”, Communs Pure and Appl. Math., 37 (1984), 539–577 | DOI | MR | Zbl