Convergence of the Spectral Decomposition of a Function from the Class W p , m 1 G , p > 1 $$ {W}_{p,m}^1(G),p>1 $$ , in the Vector Eigenfunctions of a Differential Operator of the Third Order

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 $$ \overline{G}=\left[0,1\right] $$ is estimated.