@article {
author = {Esmaeelzadeh, Fatemeh},
title = {Multi-dimensional wavelets on Sobolev spaces},
journal = {Khayyam Journal of Mathematics},
volume = {7},
number = {2},
pages = {211-218},
year = {2021},
publisher = {Department of Pure Mathematics, Ferdowsi University of Mashhad (in cooperation with the Center of Excellence in Analysis on Algebraic Structures and Tusi Mathematical Research Group)},
issn = {2423-4788},
eissn = {2423-4788},
doi = {10.22034/kjm.2021.202782.1576},
abstract = {In this paper, for admissible and integrable function $\psi$ in $L^2(\mathbb{R}^n)$, the multi-dimensional continuous wavelet transform on Sobolev spaces is defined. The inversion formula for this transform on Sobolev spaces is established and as a result it is concluded that there is an isometry of Sobolev spaces $H_s(\mathbb{R}^n)$ into $H_{0,s}(\mathbb{R}^n \times \mathbb{R}^+_0\times S^{n-1})$, for arbitrary real $s$. Also, among other things, it is shown that the range of this transform is a reproducing kernel Hilbert space and the reproducing kernel is found.},
keywords = {Sobolev space,similitude group,multidimensional wavelet,reproducing kernel},
url = {http://www.kjm-math.org/article_130075.html},
eprint = {http://www.kjm-math.org/article_130075_9a177af8e6f9787ecd973580817508db.pdf}
}