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

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 Wp,m1G,p>1, in the vector eigenfunctions of this operator is studied and the rate of uniform convergence of this expansion on G¯=01 is estimated.