id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ejpam-4006	Bupasiri, Sudprathai	On the Operator ⊕k,m Related to the Wave Equation and Laplacian	2021	14	.pdf	application/pdf	4464	303	83	Thus, equation (7) can be written as ⊕km = ( � +m2 )k (4+m2 )k ( L1 +m2 )k ( L2 +m2 )k = ( L2 +m2 )k ( L1 +m2 )k (4+m2 )k ( � +m2 )k (15) and from (7) with q = m = 0 and k = 1, we obtain Laplace operator of p-dimension ⊕0 = 44 p, where 4p = ∂2 ∂x21 + ∂2 ∂x22 + · · ·+ ∂2 ∂x2p . At first we study the fundamental solution of the operator ⊕k m and after that, we apply such the fundamental solution to solve for the solution of the equation ⊕k mu(x) = f(x), where f(x) is generalized function and u(x) is unknown function for x ∈ Rn. 2020 Mathematics Subject Classifications: 46F10 Key Words and Phrases: Wave equation, Laplace operator, Ultra-hyperbolic operator 1.	cache/ejpam-4006.pdf	txt/ejpam-4006.txt