Fourier transforms of splines and fundamental splines for cardinal Hermite interpolations
Author:
S. L. Lee
Journal:
Proc. Amer. Math. Soc. 57 (1976), 291296
MSC:
Primary 41A15; Secondary 42A68
MathSciNet review:
0420074
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Abstract: Using the exponential Hermite Euler splines we compute the Fourier transforms of the splines and fundamental splines for Cardinal Hermite Interpolation, introduced by Schoenberg and Sharma and Lipow and Schoenberg respectively.
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F. Richards, The Lebesgue constants for cardinal spline interpolation, MRC Report #1364, University of Wisconsin, 1973.
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S. D. Silliman, The numerical evaluation by splines of the Fourier transform and the Laplace transform, MRC Report #1183, University of Wisconsin, 1972.
 [1]
 P. Lipow and I. J. Schoenberg, Cardinal interpolation and spline functions. III. Cardinal Hermite interpolation, J. Linear Algebra and Appl. 6(1973), 273304. MR 0477565 (57:17084)
 [2]
 S. L. Lee, splines for cardinal Hermite interpolation, J. Linear Algebra and Appl. (to appear). MR 0382916 (52:3798)
 [3]
 , Exponential Hermite Euler splines, J. Approximation Theory (to appear). MR 0435665 (55:8623)
 [4]
 S. L. Lee and A. Sharma, Cardinal lacunary interpolation by splines. I. The characteristic polynomials, J. Approximation Theory (to appear). MR 0415141 (54:3232)
 [5]
 M. J. Marsden, F. Richards and S. Riemenschneider, Cardinal spline interpolation operators on data, Indiana Math. J. 24 (1975), 677689. MR 0382925 (52:3807)
 [6]
 I. J. Schoenberg, Contributions to the problem of approximation of equidistant data by analytic functions. Part A. On the problem of smoothing or graduation. A first class of analytic approximation formulae; Part B. On the problem of osculatory interpolation. A second class of analytic approximation formulae, Quart. Appl. Math. 4(1946), 4599, 112141. MR 7, 487; 8, 55. MR 0015914 (7:487b)
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 , Cardinal interpolation and spline functions, J. Approximation Theory 2(1969), 167206. MR 41 #2266. MR 0257616 (41:2266)
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 , Cardinal interpolation and spline functions. II, J. Approximation Theory 6(1972), 404420. MR 0340899 (49:5649)
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 , Cardinal interpolation and spline functions. IV. The exponential Euler splines, Proc. Oberwolfach Conf., 1971, ISNM 20(1972), 382402.
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 , Cardinal spline interpolation, Regional Conf. Ser. in Appl. Math., no. 12, SIAM, Philadelphia, Pa., 1973. MR 0420078 (54:8095)
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 I. J. Schoenberg and A. Sharma, Cardinal interpolation and spline functions. V. splines for cardinal Hermite interpolation, J. Linear Algebra and Appl. 7(1973), 142. MR 0477566 (57:17085)
 [12]
 F. Richards, The Lebesgue constants for cardinal spline interpolation, MRC Report #1364, University of Wisconsin, 1973.
 [13]
 S. D. Silliman, The numerical evaluation by splines of the Fourier transform and the Laplace transform, MRC Report #1183, University of Wisconsin, 1972.
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029939197604200748
PII:
S 00029939(1976)04200748
Keywords:
Fourier transforms,
spline functions,
Cardinal Hermite Interpolation
Article copyright:
© Copyright 1976
American Mathematical Society
