On Coefficients of Eigenfunction Expansions for Boundary-Value Problems with Parameter in Boundary Conditions

G. D. Birkhoff, “On asymptotic character of the solution of certain linear differential equations containing parameter,” Trans. Amer. Math. Soc., 9 (1908), 219–231. G. D. Birkhoff, “Boundary-value and expansion problems of ordinary linear differential equations,” Trans. Amer. Math. Soc., 9 (1908), 373–395. J. D. Tamarkin, On Certain General Problems in Theory of Ordinary Differential Equations and on Expansions of Arbitrary Functions in Series [in Russian], St. Petersburg, 1917. M. V. Keldysh, “On eigenvalues and eigenfunctions of certain classes of non-selfadjoint equations,” Dokl. Akad. Nauk SSSR [Soviet Math. Dokl.], 77 (1951), no. 1, 11–14. M. V. Keldysh, “On completeness of eigenfunctions for certain classes of non-selfadjoint operators,” Uspekhi Mat. Nauk [Russian Math. Surveys], 26 (1971), no. 4, 15–41. A. A. Shkalikov, “Boundary-value problems for ordinary differential equations with a parameter in boundary conditions,” [in Russian], Trudy Sem. Petrovsk. (1983), no. 9, 190–229. A. A. Shkalikov, “Elliptic equations in Hilbert space and related spectral problems,” [in Russian], Trudy Sem. Petrovsk. (1989), no. 14, 140–224. A. N. Krylov, “Certain remarks on crashers and indicators,” [in Russian], Izv. Akad. Nauk, Ser. 6, St. Petersburg, 3 (1909), no. 15, 623–654. S. V. Meleshko and Yu. V. Pokornyi, “On a vibration boundary-value problem,” Differentsialľnye Uravneniya [Differential Equations], 23 (1987), no. 8, 1466–1467. J. Walter, “Regular eigenvalue problems with eigenvalue parameter in the boundary conditions,” Math. Z., 133 (1973), no. 4, 301–312. D. B. Hinton, “An expansion theorem for an eigenvalue parameter in boundary condition,” Quart. J. Math. Oxford, 30 (1979), no. 2, 33–42. N. Yu. Kapustin and E. I. Moiseev, “On a spectral problem in theory of parabolic-hyperbolic heat equation,” Dokl. Ross. Akad. Nauk [Russian Acad. Sci. Dokl. Math.], 352 (1997), no. 4, 451–454. G. M. Gubreev and V. N. Pivovarchik, “Spectral analysis of the Regge problem with parameters,” Funktsional. Anal. i Prilozhen. [Functional Anal. Appl.], 31 (1997), no. 1, 70–74. A. G. Kostyuchenko and A. A. Shkalikov, “To theory of self-adjoint quadratic operator pencils,” Vestnik Moskov. Univ. Ser. I Mat. Mekh. [Moscow Univ. Math. Bull.], (1983), no. 6, 40–51. A. M. Akhtyamov, “On the calculation of coefficients of eigenfunction expansions with respect to the derivative chains of a spectral problem,” Mat. Zametki [Math. Notes], 51 (1992), no. 6, 137–139. A. M. Akhtyamov, “On coefficients of eigenfunction expansions for the boundary-value problem with spectral parameter in boundary condition,” Izv. Vyssh. Uchebn. Zaved. Mat. [Russian Math. (Iz. VUZ)], (2000), no. 2, 13–18.