Literature
E.I. Moissev, An asymptotic mean-value formula for a regular solution of a differential equation. Differential equations (Minsk) 16, N5, 827–844 (1980), (Russian).
V.A. Il’in, I. Joo, A uniform eigenfunction’s estimate and upper estimate for eigenvalues of a Sturm-Liouville operator with a class L p potential. Differential equations (Minsk) 15, N7, 1164–1174 (1979), (Russian).
V. Komornik, Upper estimates for the eigenf unctions of higher order linear differential operators. Acta sci. math. 45, N1-4, 261–271 (1983).
V. Komornik, Lower upper estimates for the eigenf unctions of a linear differential operator. Acta sci. math. 48, Nl-4, 243–256 (1985).
L.A. Shuster, Uniform estimates of eigenfunctions for some differential operator. Math, inst., Alma-ata, manuscript deposited at VINITI. 27.04.84, N3304-84 (Russian).
N.B. Kerimov, Some properties of the eigen- and associated functions of ordinary differential operators. Soviet Mat. Dokl. 291, N5 1054–1056 (1986) (Russian).
N.B. Kerimov, Asymptotic formulae for the eigen- and associated functions of ordinary differential operators. Moscow univ.,Moscow, manuscript deposited at VINITI 30.01.86, N663-13 B86 (Russian).
V.V. Tichomirov, Precise estimates for the eigenfunctions of an arbitrary nonselfad-joint Schrödinger operator. Differential equations (Minsk) 19,N8, 1378–1385 (1983) Russian).
I.S. Lomov, Estimates for the eigen- and associated functions of ordinary differential operators. Differential equations (Minsk) 21, N5, 903–906 (1985) (Russian).
V.A. Il’in, Necessary and sufficient conditions for a basisness of a M.V. Keldysh’s certain subsystem of eigen- and associated functions’ pencil for an ordinary differential operator. Soviet Math. Dokl. 227, N4, 796–799 (1976) (Russian).
V.A. Il’in, Necessary and sufficient conditions for a basisness and equiconvergence with a trigonometric series for spectral decompositions.I. Differential equations (Minsk) 16, N5, 771–794 (1980); II. 16,N6, 980-1009 (1980) (Russian).
V.D. Budaev, Derivative’s modulus estimates of a regular solution of ordinary differential equation. Differential equations (Minsk) 23, N2, 198–204 (1987) (Russian).
V.S. Rykhlov, On asymptotics for a system of solutions of a quasidifferential equation. Differential equations and function theory (Saratov) 5, 51–59 (1983) (Russian).
M.A. Naimark, Linear differential operators. Nauka, Moscow (1969) (Russian).
G.D. Birkhoff, On the asymptotic character of the solutions of certain linear differential equations containing a parameter. Trans. Amer. Math. Soc. 9, 219–231 (1908).
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Minkin, A. Almost orthogonality of Birkhoff’s Solutions. Results. Math. 24, 280–287 (1993). https://doi.org/10.1007/BF03322336
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DOI: https://doi.org/10.1007/BF03322336