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Expansion in eigenfunctions of a fourth-order differential operator with a piecewize constant leading coefficientстатья
Дата последнего поиска статьи во внешних источниках: 16 января 2019 г.
- Автор: Budak A.B.
- Журнал: Differential Equations
- Том: 16
- Номер: 9
- Год издания: 1981
- Издательство: Pleiades Publishing, Inc.
- Местоположение издательства: New York, USA
- Первая страница: 982
- Последняя страница: 992
- Аннотация: The author considers the fourth-order differential operator Lu = pu(4)+ (ru′)′ + q u, where p is piecewise constant, r and q are smooth functions in (a,b)\{x0}; x0 in (a,b) is a fixed point. The author examines the problem of eigenvalues and eigenfunctions of the operator L in the interval (a,b) with homogeneous boundary conditions at the points a and b. For any function f in L2(a,b), he defines a function f~ x0 (x) and proves that the expansion of f in eigenfunctions of the operator L is convergent at the point x if and only if the Fourier trigonometric series of f x 0 is convergent at x . These results generalize the results of V. A. Ilʹin [Mat. Zametki 22 (1977), no. 5, 679–698; MR0499820].
- Добавил в систему: Будак Александр Борисович