Spline Summability of Cardinal Sine Series and the Bernstein Class
作者： Wolodymyr R. Madych
DOI: 10.1007/978-3-030-12277-5_16
关键词:
摘要: In an article published in 1976, I. J. Schoenberg conjectured that if the function f is Bernstein class Bπ and Sk({f(n)}, x) piecewise polynomial cardinal spline of order 2k interpolates (n, f(n)), n = 0, ±1, ±2, … , then for some constant c $$\displaystyle\lim _{k \to \infty } S_k(\{f(n)\}, f(x) - c \sin \pi x$$ uniformly on compact subsets real axis \({\mathbb R}\).
springer.com
sci-hub.st 参考文章(12)
I. J. Schoenberg, On the Remainders and the Convergence of Cardinal Spline Interpolation for Almost Periodic Functions I. J. Schoenberg Selected Papers. pp. 137- 163 ,(1988) , 10.1007/978-1-4899-0433-1_5
J. R. Higgins, Five short stories about the cardinal series Bulletin of the American Mathematical Society. ,vol. 12, pp. 45- 89 ,(1985) , 10.1090/S0273-0979-1985-15293-0
S. D. Riemenschneider, Convergence of interpolating cardinal splines: Power growth Israel Journal of Mathematics. ,vol. 23, pp. 339- 346 ,(1976) , 10.1007/BF02761812
W.R Madych, S.A Nelson, Polyharmonic cardinal splines Journal of Approximation Theory. ,vol. 60, pp. 141- 156 ,(1990) , 10.1016/0021-9045(90)90079-6
I. J. Schoenberg, Notes on spline functions III: On the convergence of the interpolating cardinal splines as their degree tends to infinity Israel Journal of Mathematics. ,vol. 16, pp. 87- 93 ,(1973) , 10.1007/BF02761973
B.A. Bailey, W.R. Madych, Functions of exponential type and the cardinal series Journal of Approximation Theory. ,vol. 181, pp. 54- 72 ,(2014) , 10.1016/J.JAT.2014.02.003
B. A. Bailey, W. R. Madych, Convergence of Classical Cardinal Series and Band Limited Special Functions Journal of Fourier Analysis and Applications. ,vol. 19, pp. 1207- 1228 ,(2013) , 10.1007/S00041-013-9291-4
I. J. Schoenberg, Cardinal Interpolation and Spline Functions VII. the Behavior of Cardinal Spline Interpolants as their Degree Tends to Infinity I. J. Schoenberg Selected Papers. ,vol. 27, pp. 111- 135 ,(1988) , 10.1007/978-1-4899-0433-1_4
D. J. Newman, Finite Type Functions as Limits of Exponential Sums Proceedings of the American Mathematical Society. ,vol. 86, pp. 602- 604 ,(1982) , 10.1090/S0002-9939-1982-0674089-8
F. B. Richards, I. J. Schoenberg, Notes on Spline Functions IV. A Cardinal Spline Analogue of the Theorem of the Brothers Markov. Israel Journal of Mathematics. ,vol. 16, pp. 94- 102 ,(1973) , 10.1007/BF02761974