Radon Transform on Sobolev Spaces Full article
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Siberian Mathematical Journal
ISSN: 0037-4466 , E-ISSN: 1573-9260 |
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| Output data | Year: 2021, Volume: 62, Number: 3, Pages: 560-580 Pages count : 21 DOI: 10.1134/S0037446621030198 | ||
| Tags | 517.9; Radon transform; Reshetnyak formula; Sobolev spaces | ||
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Abstract:
The Radon transform R maps a function f on Rn to the family of the integrals of f over all hyperplanes. The classicalReshetnyak formula (also called the Plancherel formula for the Radon transform) states that (Formula Presented.), where(Formula Presented.) is some special norm. The formula extends the Radon transform to the bijective Hilbert space isometry (Formula Presented.).Given reals r, s, and -n/2, we introduce the Sobolev type spaces (Formula Presented.) and prove the version of the Reshetnyak formula:(Formula Presented.).The formula extends the Radon transform to the bijective Hilbert space isometry (Formula Presented.).If (Formula Presented.) are integers then (Formula Presented.) consists of the even functions ϕ(ξ, p) with square integrable derivatives of order ≤ r with respect to ξ and order ≤ s with respect to p. © 2021, Pleiades Publishing, Ltd.
Cite:
Sharafutdinov V.A.
Radon Transform on Sobolev Spaces
Siberian Mathematical Journal. 2021. V.62. N3. P.560-580. DOI: 10.1134/S0037446621030198 WOS Scopus OpenAlex
Radon Transform on Sobolev Spaces
Siberian Mathematical Journal. 2021. V.62. N3. P.560-580. DOI: 10.1134/S0037446621030198 WOS Scopus OpenAlex
Identifiers:
| Web of science: | WOS:000655743500019 |
| Scopus: | 2-s2.0-85109939228 |
| OpenAlex: | W3168099201 |