On the product of the ultra-hyperbolic bessel operator related to the elastic waves
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Date
2009
Journal Title
Journal ISSN
Volume Title
Publisher
Selcuk University Research Center of Applied Mathematics
Access Rights
info:eu-repo/semantics/openAccess
Abstract
In this article, we study the solution of the equation ?_{B,c?}^{k}?_{B,c?}^{k}u(x)=? where u(x) is an unknown generalized function and ? is a Dirac-delta function, ?_{B,c?}^{k} and ?_{B,c?}^{k} are the Ultra-Hyperbolic Bessel Operator iterated k-times and are defined by?_{B,c?}^{k} = [(1/(c?))(B_{x?}+B_{x?}++B_{x_{p}})-(B_{x_{p+1}}++B_{x_{p+q}})]^{k}?_{B,c?}^{k} = [(1/(c?))(B_{x?}+B_{x?}++B_{x_{p}})-(B_{x_{p+1}}++B_{x_{p+q}})]^{k}, where p+q=n, B_{x_{i}}=((?)/(?x_{i}))+((2v_{i})/(x_{i}))(?/(?x_{i})), where 2v_{i}=2?_{i}+1, ?_{i}>-(1/2)[6], x_{i}>0, i=1,2,...,n,c? and c? is positive constant, k is a nonnegative integer and n is the dimension of the R_{n}?. Firstly, it is found that the solution u(x) depends on the conditions of p and q and moreover such a solution is related to the solution of the Ultra-Hyperbolic Bessel Operator iterated k-times.
Description
URL: http://sjam.selcuk.edu.tr/sjam/article/view/222
Keywords
Dirac-delta distribution, Dirac-delta dağılımı, Bessel operator, Bessel operatörü, Ultra-hyperbolic bessel operator, Ultra hiperbolik bessel operatörü, Tempered distribution, Temperli dağıtım
Journal or Series
Selcuk Journal of Applied Mathematics
WoS Q Value
Scopus Q Value
Volume
10
Issue
Citation
Sağlam, A., Yıldırım, H., Sarıkaya, M. Z. (2009). On the product of the ultra-hyperbolic bessel operator related to the elastic waves. Selcuk Journal of Applied Mathematics, 10 (1), 85-93.
