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Creators/Authors contains: "Mishra, Rohit Kumar"

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  1. ; ; (, Inverse Problems)
    Abstract We 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. 
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  2. ; (, Journal of Spectral Theory)
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