2017
Том 69
№ 9

All Issues

Convergence of the spectral decomposition of a function from the class $W_{p,m}^1 (G),\; p > 1$, in the vector eigenfunctions of a differential operator of the third order

Abbasova Yu. G., Kurbanov V. M.


Abstract

We consider, a third-order differential operator with matrix coefficients. The absolute and uniform convergence of the orthogonal expansion of a vector function from the class $W_{p,m}^1 (G),\; p > 1$, in the vector eigenfunctions of this operator is studied and the rate of uniform convergence of this expansion on $G = [0, 1]$ is estimated.

Citation Example: Abbasova Yu. G., Kurbanov V. M. Convergence of the spectral decomposition of a function from the class $W_{p,m}^1 (G),\; p > 1$, in the vector eigenfunctions of a differential operator of the third order // Ukr. Mat. Zh. - 2017. - 69, № 6. - pp. 719-733.