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


MSC:

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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References:

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[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 · doi:10.1016/0022-247X(78)90214-7
[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 · doi:10.1215/S0012-7094-75-04256-8
[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) · doi:10.1007/BF01435415
[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 · doi:10.1090/S0002-9904-1977-14406-6
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