Asymptotic expansions of multiple integrals of rapidly oscillating functions
T. Iwaniec and A. Lutoborski
Math. Comp. 50 (1988), 215-228
Full-text PDF Free Access
Similar Articles |
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.
M. Abramowitz & I. A. Stegun, Handbook of Mathematical Functions, Dover, New York, 1972.
J. Lardy, and A.
Lutoborski, Asymptotic expansions of integrals of
certain rapidly oscillating functions, Math.
Comp. 49 (1987), no. 179, 243–249. MR 890265
Lions, and George
Papanicolaou, Asymptotic analysis for periodic structures,
Studies in Mathematics and its Applications, vol. 5, North-Holland
Publishing Co., Amsterdam-New York, 1978. MR 503330
J. Davis and Philip
Rabinowitz, Methods of numerical integration, 2nd ed.,
Computer Science and Applied Mathematics, Academic Press, Inc., Orlando,
FL, 1984. MR
N. Lyness, The calculation of Fourier
coefficients by the Möbius inversion of the Poisson summation formula.
I. Functions whose early derivatives are continuous, Math. Comp. 24 (1970), 101–135. MR 0260230
(41 #4858), http://dx.doi.org/10.1090/S0025-5718-1970-0260230-8
J. Stetter, Numerical approximation of Fourier-transforms,
Numer. Math. 8 (1966), 235–249. MR 0198716
Talenti, Best constant in Sobolev inequality, Ann. Mat. Pura
Appl. (4) 110 (1976), 353–372. MR 0463908
- M. Abramowitz & I. A. Stegun, Handbook of Mathematical Functions, Dover, New York, 1972.
- U. Banerjee, L. J. Lardy & A. Lutoborski, "Asymptotic expansions of integrals of certain rapidly oscillating functions," Math. Comp., v. 49, 1987, pp. 243-249. MR 890265 (88e:41063)
- A. Bensoussan, J. L. Lions & G. Papanicolaou, Asymptotic Analysis of Periodic Structures, North-Holland, Amsterdam, 1978. MR 503330 (82h:35001)
- P. J. Davis & P. Rabinowitz, Methods of Numerical Integration, 2nd ed., Academic Press, New York, 1984. MR 760629 (86d:65004)
- 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. 101-135. MR 0260230 (41:4858)
- H. J. Stetter, "Numerical approximation of Fourier transforms," Numer. Math., v. 8, 1966, pp. 235-249. MR 0198716 (33:6870)
- G. Talenti, "Best constant in Sobolev inequality," Ann. Mat. Pura Appl., v. 110, 1976, pp. 353-372. MR 0463908 (57:3846)
Retrieve articles in Mathematics of Computation
Retrieve articles in all journals
© Copyright 1988
American Mathematical Society