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]**Peter R. Lipow and I. J. Schoenberg,*Cardinal interpolation and spline functions. III. Cardinal Hermite interpolation*, Linear Algebra and Appl.**6**(1973), 273–304. MR**0477565****[2]**S. L. Lee,*𝐵-splines for cardinal Hermite interpolation*, Linear Algebra and Appl.**12**(1975), no. 3, 269–280. MR**0382916****[3]**S. L. Lee,*Exponential Hermite-Euler splines*, J. Approximation Theory**18**(1976), no. 3, 205–212. MR**0435665****[4]**S. L. Lee and A. Sharma,*Cardinal lacunary interpolation by 𝑔-splines. I. The characteristic polynomials*, J. Approximation Theory**16**(1976), no. 1, 85–96. MR**0415141****[5]**M. J. Marsden, F. B. Richards, and S. D. Riemenschneider,*Cardinal spline interpolation operators on 𝑙^{𝑝} data*, Indiana Univ. Math. J.**24**(1974/75), 677–689. MR**0382925**, https://doi.org/10.1512/iumj.1975.24.24052**[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*, Quart. Appl. Math.**4**(1946), 45–99. MR**0015914**, https://doi.org/10.1090/S0033-569X-1946-15914-5**[7]**I. J. Schoenberg,*Cardinal interpolation and spline functions*, J. Approximation Theory**2**(1969), 167–206. MR**0257616****[8]**I. J. Schoenberg,*Cardinal interpolation and spline functions. II. Interpolation of data of power growth*, J. Approximation Theory**6**(1972), 404–420. Collection of articles dedicated to J. L. Walsh on his 75th birthday, VIII. MR**0340899****[9]**-,*Cardinal interpolation and spline functions*. IV.*The exponential Euler splines*, Proc. Oberwolfach Conf., 1971, ISNM**20**(1972), 382-402.**[10]**I. J. Schoenberg,*Cardinal spline interpolation*, Society for Industrial and Applied Mathematics, Philadelphia, Pa., 1973. Conference Board of the Mathematical Sciences Regional Conference Series in Applied Mathematics, No. 12. MR**0420078****[11]**I. J. Schoenberg and A. Sharma,*Cardinal interpolation and spline functions. V. The 𝐵-splines for cardinal Hermite interpolation*, Linear Algebra and Appl.**7**(1973), 1–42. MR**0477566****[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