Sums of plane waves, and the range of the Radon transform. (English) Zbl 0424.35005


35A22 Transform methods (e.g., integral transforms) applied to PDEs
35L05 Wave equation
46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
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[1] Adams, R., Aronszajn, N., Smith, K.T.: Theory of Bessel potentials, Part II. Ann. Inst. Fourier (Grenoble)17, 1-135 (1967) · Zbl 0185.19703
[2] Ehrenpreis, L.: Fourier analysis in several complex variables. In: Pure and applied mathematics, XVII. New York: Wiley-Interscience 1970 · Zbl 0195.10401
[3] Falconer, K.J.: Consistency conditions for a finite set of projections of a function. Math. Proc. Cambridge Philos. Soc.85, 61-68 (1979) · Zbl 0386.28008
[4] Hamaker, C., Solmon, D.C.: The angles between the null spaces ofx-rays. J. Math. Anal. Appl.62, 1-23 (1978) · Zbl 0437.45025
[5] Hormander, L.: An introduction to complex analysis in several variables. Amsterdam, London, New York: North-Holland-American Elsevier 1973
[6] Logan, B.F., Shepp, L.A.: Optimal reconstruction of a function from its projections. Duke Math. J.42, 645-659 (1975) · Zbl 0343.41020
[7] Malgrange, B.: Sur les systemes differentiels a coefficients constants. Sem. sur les equations aux derivees partielles, College de France, 1961-2
[8] Smith, K.T.: Formulas to represent functions by their derivatives. Math. Ann.188, 53-77 (1970) · Zbl 0194.41303
[9] Smith, K.T., Solmon, D.C., Wagner, S.L.: Practical and mathematical aspects of reconstructing objects from radiographs. Bull. Amer. Math. Soc.83, 1227-1270 (1978) · Zbl 0521.65090
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