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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th-cmuir.6653943832-429542017-09-28T06:44:22Z Cauchy problem of the Δ(<sup>k</sup>) operator related to the Diamond operator and the Laplace operator iterated k times Bunpog C. 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. 2017-09-28T06:44:22Z 2017-09-28T06:44:22Z 2011-12-01 Journal 15211398 2-s2.0-84885335136 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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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. |
| format |
Journal |
| author |
Bunpog C. |
| spellingShingle |
Bunpog C. Cauchy problem of the Δ(<sup>k</sup>) operator related to the Diamond operator and the Laplace operator iterated k times |
| author_facet |
Bunpog C. |
| author_sort |
Bunpog C. |
| title |
Cauchy problem of the Δ(<sup>k</sup>) operator related to the Diamond operator and the Laplace operator iterated k times |
| title_short |
Cauchy problem of the Δ(<sup>k</sup>) operator related to the Diamond operator and the Laplace operator iterated k times |
| title_full |
Cauchy problem of the Δ(<sup>k</sup>) operator related to the Diamond operator and the Laplace operator iterated k times |
| title_fullStr |
Cauchy problem of the Δ(<sup>k</sup>) operator related to the Diamond operator and the Laplace operator iterated k times |
| title_full_unstemmed |
Cauchy problem of the Δ(<sup>k</sup>) operator related to the Diamond operator and the Laplace operator iterated k times |
| title_sort |
cauchy problem of the δ(<sup>k</sup>) operator related to the diamond operator and the laplace operator iterated k times |
| publishDate |
2017 |
| url |
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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1681422287276867584 |