Helmholtz operators on infinite graphs

Abstract

The Helmholtz equation in its simplest form is Δu(a)=−k2u(a). In this note, we study a generalized discrete version of this equation on an infinite graph, by using potential-theoretic methods.

Keywords

• Helmholtz infinite network
• HH-superharmonic
• HH-hyperbolic
• HH-parabolic
• Choquet theorem
• Cartesian product