## Expansion in eigenfunctions of a fourth-order differential operator with a piecewize constant leading coefficientстатья

Статья опубликована в журнале из списка Web of Science и/или Scopus
Дата последнего поиска статьи во внешних источниках: 16 января 2019 г.
• Автор:
• Журнал: Differential Equations
• Том: 16
• Номер: 9
• Год издания: 1981
• Издательство: Maik Nauka/Interperiodica Publishing
• Местоположение издательства: Russian Federation
• 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

### Работа с статьей

 [1] Budak A. B. Expansion in eigenfunctions of a fourth-order differential operator with a piecewize constant leading coefficient // Differential Equations. — 1981. — Vol. 16, no. 9. — P. 982–992. 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].