Cauchy problem of the Δ(<sup>k</sup>) operator related to the Diamond operator and the Laplace operator iterated k times
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 particul...
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| Format: | Journal |
| Published: |
2017
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| Online Access: | https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=84885335136&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/42954 |
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| Institution: | Chiang Mai University |
| Summary: | 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. |
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