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In this paper we study a Cauchy problem of the diamond operator iterated k−times, denoted by ♦ k which is defined by where k is the Laplace operator iterated k−times and 2 k is the ultrahyperbolic operator iterated k−times. The existence of a solution of a Cauchy problem of the diamond operator iterated k−times is proven. Mathematics Subject Classification: 46F10doi:10.12988/ijma.2013.36134 fatcat:ufjhpny6evhznjtdhu27axus5i