Mishra, Rohit KumarRohit KumarMishraMonard, FrancoisFrancoisMonardZou, YuzhouYuzhouZou2025-08-282025-08-282022-03-01http://arxiv.org/abs/2203.09861https://d8.irins.org/handle/IITG2025/20104We study various self-adjoint realizations of the X-ray transform on the Euclidean disk D, obtained by considering specific singularly weighted L2 topologies. We first recover the well-known Singular Value Decompositions in terms of disk orthogonal polynomials, then prove that each such realization is an isomorphism of C?(D). As corollaries: we give some range characterizations; we explain how for such choices, these normal operators are in the functional calculus of two distinguished differential operators; we show that the isomorphism property also holds on a class of constant-curvature, circularly symmetric simple surfaces.en-USAnalysis of PDEsSpectral TheoryC?Euclidean disk DL2 topologyorthogonal polynomialse-Printe-Print123456789/555