Inversion formulas for complex Radon transform on projective varieties\n and boundary value problems for systems of linear PDE

2011/06/14 by Gennadi M. Henkin, Henkin, Gennadi M., Peter L. Polyakov +1
Computer Science · Earth and Planetary Sciences · Engineering · Mathematics · #Advanced Numerical Analysis Techniques #Complex Variables (math.CV) #FOS: Mathematics #Mathematical Analysis and Transform Methods #Polynomial and algebraic computation #Seismic Imaging and Inversion Techniques

paper · pdf · doi:10.48550/arxiv.1106.2795

openalex publication_date 2011/06/14 · openalex created_date 2022/09/05 · openalex updated_date 2026/07/28

Abstract

Let G\⊂ C Pⁿ be a linearly convex compact with smooth boundary,\nD= CPⁿ\∖ G, and let D^* \⊂ ( C Pⁿ)^* be the dual domain.\nThen for an algebraic, not necessarily reduced, complete intersection\nsubvariety V of dimension d we construct an explicit inversion formula for\nthe complex Radon transform R_V: H^d,d-1(V\∩ D)\→ H^1,0(D^*), and\nexplicit formulas for solutions of an appropriate boundary value problem for\nthe corresponding system of differential equations with constant coefficients\non D^*.\n

Citations

• Resolution of Singularities of an Algebraic Variety Over a Field of Characteristic Zero: I

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