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The eigenfunctions of the fourthorder ordinary differential operator are estimated on a finite interval. These estimates and theorem of Il'in basis property are used to prove the basis property of a minimal and closed in Lp and normalized in L2 system of eigenfunctions corresponding to the arbitrary selfadjoint expansion of the abovementioned operator in Lp spaces.

vestnik moskovskogo gosudarstvennogo oblastnogo universiteta. seriâ fizika-matematika

ESTIMATIONS OF EIGENFUNCTIONS OF ORDINARY FOURTH-ORDER DIFFERENTIAL OPERATOR AND THEIR USE WHEN CHECKING THE BASIS PROPERTY CONDITION BY V.A. IL'IN IN L p SPACES