Rocky Mountain Journal of Mathematics

Linear Independence of the Translates of an Exponential Box Spline

Amos Ron

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Rocky Mountain J. Math., Volume 22, Number 1 (1992), 331-351.

First available in Project Euclid: 5 June 2007

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Ron, Amos. Linear Independence of the Translates of an Exponential Box Spline. Rocky Mountain J. Math. 22 (1992), no. 1, 331--351. doi:10.1216/rmjm/1181072814.

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  • C. de Boor, The polynomials in the linear span of integer translates of a compactly supported function, Constr. Approx. 3 (1987), 199-208.
  • C. de Boor and R. DeVore, Approximation by smooth multivariate splines, Trans. Amer. Math. Soc. 276 (1983), 775-788.
  • C. de Boor and K. Höllig, B-splines from parallelepipeds, J. Analyse Math. 42 (1982/3), 99-115.
  • C. de Boor and R.Q. Jia, Controlled approximation and a characterization of the local approximation order, Proc. Amer. Math. Soc. 95 (1985), 547-553.
  • A. Ben-Artzi and A. Ron, Translates of exponential box splines and their related spaces, Trans. Amer. Math. Soc. 309 (1988), 683-710.
  • C.K. Chui, K. Jetter and J.D. Ward, Cardinal interpolation by multivariate splines, Math. Comp. 48 (1987), 711-724.
  • C.K. Chui and M.J. Lai, A multivariate analog of Marsden's identity and a quasiinterpolation scheme, Constr. Approx. 3 (1987), 111-122.
  • W. Dahmen and C.A. Micchelli, Translates of multivariate splines, Linear Algebra Appl. 52/3 (1983), 217-234.
  • --------, On the approximation order from certain multivariate spline spaces, J. Austral. Math. Soc. Ser B 26 (1984), 233-246.
  • --------, Recent progress in multivariate splines, in Approximation theory IV (C.K. Chui, L.L. Schumaker and J.D. Ward, eds.), Academic Press, New York, 1983, 27-121.
  • --------, On the local linear independence of translates of a box spline, Studia Math. 82 (1985), 243-263.
  • --------, On the solution of certain systems of partial difference equations and linear dependence of translates of box splines, Trans. Amer. Math. Soc. 292 (1985), 305-320.
  • --------, On multivariate E-splines, Adv. Math. 76 (1989), 33-93.
  • I.M. Gelfand and G.E. Shilov, Generalized functions, Vol. 2, Academic Press, New York, 1968.
  • R.Q. Jia, On the linear independence of translates of box splines, J. Approx. Theory 40 (1984), 158-160.
  • --------, Local linear independence of the translates of a box spline, Constr. Approx. 1 (1985), 175-182.
  • M.J. Marsden, An identity for spline functions with applications to variation diminishing spline approximation, J. Approx. Theory 3 (1970), 7-49.
  • A. Ron, Exponential box splines, Constr. Approx. 4 (1988), 357-378.
  • --------, On exponential box splines and other types of nonpolynomial B-splines, Thesis, Tel-Aviv Univ., March 1987.
  • I.J. Schoenberg, Contributions to the problem of approximation of equidistant data by analytic functions A, Quart. Appl. Math. 4 (1946), 45-99.
  • L.L. Schumaker, Spline functions basic theory, John Wiley & Sons, New York, 1981.
  • G. Strang and G. Fix, A Fourier analysis of the finite element variational method. C.I.M.E. II Ciclo 1971, Constructive Aspects of Functional Analysis (G. Geymona, ed.), 1973, 793-840.