On the Green function of the (⊕+m2)k operator
In this article, we study the Green function of the operator (⊕+m2)k which is iterated k-times and is defined by equation presented where m is a positive real number and p+q=n is the dimension of the n-dimensional Euclidean space ℝn, x=(x1, x2,.., xn)ε ℝn and k is a nonnegative integer. At first, we...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
2014
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| Online Access: | http://www.scopus.com/inward/record.url?eid=2-s2.0-33947511621&partnerID=40&md5=631f7ab732a363cbb6862602a3a82849 http://cmuir.cmu.ac.th/handle/6653943832/5331 |
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| Institution: | Chiang Mai University |
| Language: | English |
| Summary: | In this article, we study the Green function of the operator (⊕+m2)k which is iterated k-times and is defined by equation presented where m is a positive real number and p+q=n is the dimension of the n-dimensional Euclidean space ℝn, x=(x1, x2,.., xn)ε ℝn and k is a nonnegative integer. At first, we study the elementary solution or Green function of the operator (⊕+m2)k. Moreover, the operator (⊕+m2)k can be related to the ultra-hyperbolic Klein-Gordon operator (□+m2)k, the Helmholtz operator (□+m2)k and the diamond operator of the form (δ+m2)k, and also we obtain the elementary solutions of such operators. We also apply such a Green function to obtain the solution of the equation (⊕+m2)kU(x)=f(x), where f is a generalized function and U(x) is an unknown function for x ε ℝn. |
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