On extensions of positive definite integral Fredholm operators

Abstract.

The main result of this paper states that a positive definite Fredholm integral operator acting on L ²([0,1]) can be modified on a Lebesque measurable set $\mit\Delta$ in [0,1]² such that the resulting operator is positive definite and its resolvent kernel is zero on $\mit\Delta$. This answers a question raised in [3]. The proof is based on extension results for positive definite operator matrices and their connection to generalized determinants.