Expansion in eigenfunctions of a fourth-order differential operator with discontinuous coefficients. (Russian)статья
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Аннотация:This paper contains some interesting results on the convergence of the expansion of an arbitrary function in a series of eigenfunctions of a general fourth-order selfadjoint differential operator on the finite interval (a,b) in the case when the coefficients of the differential equation have a jump discontinuity at x0 in (a,b) An estimate of the spectral function of this eigenvalue problem is also obtained. When reading this work, it is necessary to refer constantly to the previous paper of the author [same journal 16 (1981), no. 11, 1233–1242] in which the statement of the problem was formulated.