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Multivariate interpolation and the Radon transform. (English) Zbl 0425.46054


MSC:

46M35 Abstract interpolation of topological vector spaces
44A15 Special integral transforms (Legendre, Hilbert, etc.)
46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
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References:

[1] Ferguson, D.: The question of uniqueness for G.D. Birkhoff interpolation problems. J. Approximation Theory2, 1-28 (1969) · Zbl 0182.39202 · doi:10.1016/0021-9045(69)90028-8
[2] Gel’fand, I.M., Graev, M.I., Vilenkin, N.Ya.: Generalized Functions, Vol. V. New York-London: Academic Press 1964
[3] Gelfond, A.: Differenzenrechnung. Berlin: VEB Deutscher Verlag der Wissenschaften 1958
[4] Kergin, P.: A natural interpolation ofC k functions. J. Approximation Theory (to appear) · Zbl 0492.41008
[5] Ludwig, O.: The Radon transform on Euclidean space. Comm. Pure. Appl. Math.19, 49-81 (1966) · Zbl 0134.11305 · doi:10.1002/cpa.3160190105
[6] Micchelli, Ch.A.: A constructive approach to Kergin interpolation inR k : MultivariateB-splines and Lagrange interpolation. Rocky Mountain J. Math. (to appear)
[7] Micchelli, Ch.A., Milman, P.: A formula for Kergin interpolation inR k . J. Approximation Theory (to appear) · Zbl 0454.41002
[8] Pólya, G.: Bemerkungen zur Interpolation und zur Näherungstheorie der Balken-Biegung. Z. Angew. Math. Mech.11, 445-449 (1931) · JFM 57.1058.01 · doi:10.1002/zamm.19310110620
[9] Salzer, H.E.: Some divided difference algorithms for two variables. In: On Numerical Approximation (Ed. R.E. Langer), pp. 61-98. Madison: University of Wisconsin Press 1959 · Zbl 0086.11302
[10] Widder, D.V.: The Laplace transform. Princeton: Princeton University Press 1941 · Zbl 0063.08245
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