Approximate solution of an initial value problem by generalized cardinal series
Author:
H. D. Brunk
Journal:
Quart. Appl. Math. 11 (1953), 285-294
MSC:
Primary 65.0X
DOI:
https://doi.org/10.1090/qam/57635
MathSciNet review:
57635
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E. T. Whittaker, On the functions which are represented by the expansions of the interpolation-theory, Proc. Roy. Soc. Edinburgh, 35, 181-194 (1915).
J. M. Whittaker, Interpolatory function theory, Camb. Univ. Press, 1935.
. W. L. Ferrar, On the cardinal function of interpolation-theory, Proc. Roy. Soc. Edinburgh, 45, 269-282 (1925); 46, 323-333 (1925).
. W. L. Ferrar, On the consistency of cardinal function interpolation, Proc. Roy. Soc. Edinburgh, 49, 230-242 (1927).
- G. H. Hardy, Notes on special systems of orthogonal functions. IV. The orthogonal functions of Whittaker’s cardinal series, Proc. Cambridge Philos. Soc. 37 (1941), 331–348. MR 5145, DOI https://doi.org/10.1017/s0305004100017977
. C. -J. de la Vallée Poussin, Sur la convergence des formules d’interpolation entre ordonnées équidistantes, Bull. Acad. Roy. de Belg., Classe de Sci., 1, 319-410 (1908).
- G. H. Hardy and W. W. Rogosinski, Fourier series, Cambridge Tracts in Mathematics and Mathematical Physics, no. 38, Cambridge, At the University Press, 1950. 2nd ed. MR 0044660
. S. Bochner, Vorlesungen über Fouriersche Integrale, Leipzig, 1932.
E. T. Whittaker, On the functions which are represented by the expansions of the interpolation-theory, Proc. Roy. Soc. Edinburgh, 35, 181-194 (1915).
J. M. Whittaker, Interpolatory function theory, Camb. Univ. Press, 1935.
. W. L. Ferrar, On the cardinal function of interpolation-theory, Proc. Roy. Soc. Edinburgh, 45, 269-282 (1925); 46, 323-333 (1925).
. W. L. Ferrar, On the consistency of cardinal function interpolation, Proc. Roy. Soc. Edinburgh, 49, 230-242 (1927).
. G. H. Hardy, Notes on special systems of orthogonal functions. IV. The orthogonal functions of Whittaker’s cardinal series, Proc. Camb. Philos. Soc., 37, 331-348 (1941).
. C. -J. de la Vallée Poussin, Sur la convergence des formules d’interpolation entre ordonnées équidistantes, Bull. Acad. Roy. de Belg., Classe de Sci., 1, 319-410 (1908).
. G. H. Hardy and W. W. Rogosinski, Fourier series, Camb. Univ. Press, 1950.
. S. Bochner, Vorlesungen über Fouriersche Integrale, Leipzig, 1932.
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Article copyright:
© Copyright 1953
American Mathematical Society