1. Neural networks with Hilbert-space inputs
This chapter is Section 2 of the manuscript together with Appendix F. The input space H is a
separable real Hilbert space, the output space Y a separable complex Hilbert space, and a
network is a superposition of ridge functions x\mapsto\beta(\langle a,x\rangle+c). Section 2
defines the finite-width and the integral networks; Appendix F shows that networks with
operator-valued parameters reduce exactly to them.