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.
Esmaeelzadeh, F. (2021). Multi-dimensional wavelets on Sobolev spaces. Khayyam Journal of Mathematics, 7(2), 211-218. doi: 10.22034/kjm.2021.202782.1576
MLA
Fatemeh Esmaeelzadeh. "Multi-dimensional wavelets on Sobolev spaces". Khayyam Journal of Mathematics, 7, 2, 2021, 211-218. doi: 10.22034/kjm.2021.202782.1576
HARVARD
Esmaeelzadeh, F. (2021). 'Multi-dimensional wavelets on Sobolev spaces', Khayyam Journal of Mathematics, 7(2), pp. 211-218. doi: 10.22034/kjm.2021.202782.1576
VANCOUVER
Esmaeelzadeh, F. Multi-dimensional wavelets on Sobolev spaces. Khayyam Journal of Mathematics, 2021; 7(2): 211-218. doi: 10.22034/kjm.2021.202782.1576
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