Complete orthonormal sequences of functions uniformly small on a subset

Abstract

where [ck,,(w) ]indicates the complex conjugate of [Ec,,(w)], (cf. [1, pp. 6 and 9]). Let K be a given compact subset of D. Then we might wish to try to approximate the kernel function in K by using a finite series. Because of (2) and the fact that mD(z) is continuous, it is clear that given an e >0 and a complete orthonormal sequence {I ,, }, there exists an N= N(D, K, c, {IO,,) such that m? N and z, wEK implies