Abstract
A class of Wiener-Hopf integral operators, with kernels vanishing along the positive real axis, is obtained from considering weighted transaxial line-integrals of rotationally symmetric functions defined on ℝ2. An analysis of these operators is given when acting in, the Hilbert space L2(ℝ+). A necessary and sufficient condition for injectivity is established and inversion formulas are provided in some cases. A specific operator falling into this class, the so-called incomplete Abel transform., is presented and an inversion formula is given. This inversion formula makes precise a formal result previously established in Dallaset al. [J. Opt. Soc. Am. A4, 2039 (1987)] and it is also shown to be consistent with an inversion formula derived by Hansen [J. Opt. Soc. Am. A9, 2126 (1992)].
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This research was supported by NIH/NCI Grant R01 CA49261