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: | Journal |
| Published: |
2018
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| Subjects: | |
| Online Access: | https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=33947511621&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/61223 |
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| Institution: | Chiang Mai University |
| 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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