Asymptotic expansions of multiple integrals of rapidly oscillating functions
Authors:
T. Iwaniec and A. Lutoborski
Journal:
Math. Comp. 50 (1988), 215228
MSC:
Primary 41A60
MathSciNet review:
917829
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Abstract: Expansions of multiple integrals where w is a function on which is periodic in the kth variable, , and g is smooth, are given in terms of negative powers of the integers . Estimates of the remainder term in the expansion are also given.
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 [1]
 M. Abramowitz & I. A. Stegun, Handbook of Mathematical Functions, Dover, New York, 1972.
 [2]
 U. Banerjee, L. J. Lardy & A. Lutoborski, "Asymptotic expansions of integrals of certain rapidly oscillating functions," Math. Comp., v. 49, 1987, pp. 243249. MR 890265 (88e:41063)
 [3]
 A. Bensoussan, J. L. Lions & G. Papanicolaou, Asymptotic Analysis of Periodic Structures, NorthHolland, Amsterdam, 1978. MR 503330 (82h:35001)
 [4]
 P. J. Davis & P. Rabinowitz, Methods of Numerical Integration, 2nd ed., Academic Press, New York, 1984. MR 760629 (86d:65004)
 [5]
 J. N. Lyness, "The calculation of Fourier coefficients by the Möbius inversion of the Poisson summation formula, Part I. Functions whose early derivatives are continuous," Math. Comp., v. 24, 1970, pp. 101135. MR 0260230 (41:4858)
 [6]
 H. J. Stetter, "Numerical approximation of Fourier transforms," Numer. Math., v. 8, 1966, pp. 235249. MR 0198716 (33:6870)
 [7]
 G. Talenti, "Best constant in Sobolev inequality," Ann. Mat. Pura Appl., v. 110, 1976, pp. 353372. MR 0463908 (57:3846)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718198809178296
PII:
S 00255718(1988)09178296
Article copyright:
© Copyright 1988 American Mathematical Society
