%0 Journal Article
%T Multi-dimensional wavelets on Sobolev spaces
%J Khayyam Journal of Mathematics
%I 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)
%Z 2423-4788
%A Esmaeelzadeh, Fatemeh
%D 2021
%\ 07/01/2021
%V 7
%N 2
%P 211-218
%! Multi-dimensional wavelets on Sobolev spaces
%K Sobolev space
%K similitude group
%K multidimensional wavelet
%K reproducing kernel
%R 10.22034/kjm.2021.202782.1576
%X 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 $H_{0,s}(mathbb{R}^n times mathbb{R}^+_0times S^{n-1})$, 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.
%U http://www.kjm-math.org/article_130075_9a177af8e6f9787ecd973580817508db.pdf