Fourier transforms of -splines and fundamental splines for cardinal Hermite interpolations

Author:
S. L. Lee

Journal:
Proc. Amer. Math. Soc. **57** (1976), 291-296

MSC:
Primary 41A15; Secondary 42A68

DOI:
https://doi.org/10.1090/S0002-9939-1976-0420074-8

MathSciNet review:
0420074

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Abstract | References | Similar Articles | Additional Information

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.

**[1]**P. Lipow and I. J. Schoenberg,*Cardinal interpolation and spline functions*. III.*Cardinal Hermite interpolation*, J. Linear Algebra and Appl.**6**(1973), 273-304. 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), 677-689. 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), 45-99, 112-141. MR**7**, 487;**8**, 55. MR**0015914 (7:487b)****[7]**-,*Cardinal interpolation and spline functions*, J. Approximation Theory**2**(1969), 167-206. MR**41**#2266. MR**0257616 (41:2266)****[8]**-,*Cardinal interpolation and spline functions*. II, J. Approximation Theory**6**(1972), 404-420. MR**0340899 (49:5649)****[9]**-,*Cardinal interpolation and spline functions*. IV.*The exponential Euler splines*, Proc. Oberwolfach Conf., 1971, ISNM**20**(1972), 382-402.**[10]**-,*Cardinal spline interpolation*, Regional Conf. Ser. in Appl. Math., no. 12, SIAM, Philadelphia, Pa., 1973. MR**0420078 (54:8095)****[11]**I. J. Schoenberg and A. Sharma,*Cardinal interpolation and spline functions*. V.*-splines for cardinal Hermite interpolation*, J. Linear Algebra and Appl.**7**(1973), 1-42. 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:
https://doi.org/10.1090/S0002-9939-1976-0420074-8

Keywords:
Fourier transforms,
spline functions,
Cardinal Hermite Interpolation

Article copyright:
© Copyright 1976
American Mathematical Society