Cauchy problem of the Δ(k) operator related to the Diamond operator and the Laplace operator iterated k times - Bunpog C. (2017)
Given the Laplace operator Δ is defined by the Ultra-hyperbolic operator iterated k times k is defined by where p + q = n is the dimension of the Euclidean space ℝ n . In this paper, we study Cauchy problem and fundamental solution of the Δ( k ) operator by using Green's identity, In particular, Δ( k ) reduces to the Diamond operator if k = 1. Moreover, for q = 0 the ultra-hyperbolic operator 2 reduces to Δ, and Δ( k-1 ) reduces to the Laplace operator Δk iterated k times. © 2011 by Eudoxus Press,LLC All rights reserved.