The Radon transform on a family of curves in the plane. II

Cormack, A. M.

doi:10.1090/S0002-9939-1982-0667292-4

The Radon transform on a family of curves in the plane. II
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by A. M. Cormack PDF

Proc. Amer. Math. Soc. 86 (1982), 293-298 Request permission

Abstract:

A further discussion of Radon’s problem for curves in the plane given, for fixed $(p,\phi )$, by ${r^\alpha }\cos \{ \alpha (\theta - \phi )\} = {p^\alpha }$. $\alpha$ real, $\alpha \ne 0$. Functions yielding null transforms, and zeros of the Fourier components of the transforms are given for general $\alpha$. and several orthogonal expansions are given for $\alpha = \pm 1/m$. $m = 1,2,3 \ldots .$

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