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 L2([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.