Mishra, Rohit KumarRohit KumarMishraMonard, Fran�oisFran�oisMonardZou, YuzhouYuzhouZou2025-08-312025-08-312023-02-0110.1088/1361-6420/aca8cb2-s2.0-85145008009http://repository.iitgn.ac.in/handle/IITG2025/26907We study a one-parameter family of self-adjoint normal operators for the x-ray transform on the closed Euclidean disk D , obtained by considering specific singularly weighted L ² topologies. We first recover the well-known singular value decompositions in terms of orthogonal disk (or generalized Zernike) polynomials, then prove that each such realization is an isomorphism of C ∞ ( D ) . As corollaries: we give some range characterizations; we show how such choices of normal operators can be expressed as functions of two distinguished differential operators. We also show that the isomorphism property also holds on a class of constant-curvature, circularly symmetric simple surfaces. These results allow to design functional contexts where normal operators built out of the x-ray transform are provably invertible, in Fréchet and Hilbert spaces encoding specific boundary behavior.falsemapping properties | range characterization | singular value decomposition | x-ray transformArticle13616420February 20232024001arJournal2WOS:000921371700001