Title

Range of the radon transform on functions which do not decay fast at infinity

Keywords

Asymptotic expansion; Moment conditions; Radon transform; Range

Abstract

Let an integer m ≥ 0 be fixed. Let Xm be the space of functions f ∈ C∞(ℝn) that admit an asymptotic expansion f(rβ) ∼ ∑∞k=m ψk(β)/rn+k, r → ∞, ψk ∈ C∞(Sn-1), and the expansion can be differentiated with respect to x = rβ any number of times. In this paper, we derive a precise characterization of the range of the Radon transform R acting on Xm; that is, we explicitly describe the space Zm = RXm. The conditions which describe the space Zm are easily verifiable.

Publication Date

1-1-1997

Publication Title

SIAM Journal on Mathematical Analysis

Volume

28

Issue

4

Number of Pages

852-866

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1137/S0036141095289518

Socpus ID

0031491008 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/0031491008

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