On holomorphic solutions of the heat equation with a Volterra operator coefficient - Vershynina, A.; Gefter, S. (Methods of Functional Analysis and Topology, 2007)
Let A be a bounded operator on a Hilbert space and g a vector-valued function, which is holomorphic in a neighborhood of zero. The question about existence of holomorphic solutions of the Cauchy problem { arrayll ut= A^2ux^2 u(0,x)=g(x) array . is considered in the paper.