کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4605570 | 1337583 | 2010 | 23 صفحه PDF | دانلود رایگان |
![عکس صفحه اول مقاله: Non-Haar p-adic wavelets and their application to pseudo-differential operators and equations Non-Haar p-adic wavelets and their application to pseudo-differential operators and equations](/preview/png/4605570.png)
In the present paper an infinite family of new compactly supported non-Haar p-adic wavelet bases in is constructed. These bases cannot be constructed in the framework of any of known theories. We use the wavelet bases in the following applications: in the theory of p-adic pseudo-differential operators and equations. The connections between wavelet analysis and spectral analysis of p-adic pseudo-differential operators is studied. We derive a criterion for a multidimensional p-adic wavelet function to be an eigenfunction for a pseudo-differential operator and prove that our wavelets are eigenfunctions of the fractional operator. p-Adic wavelets are used to construct solutions of linear (the first and second order in t) and semi-linear evolutionary pseudo-differential equations. Since many p-adic models use pseudo-differential operators (fractional operator), our results can be intensively used in these models.
Journal: Applied and Computational Harmonic Analysis - Volume 28, Issue 1, January 2010, Pages 1-23