Estimates of one-dimensional oscillatory integrals

Detlef Muller

Annales de l'institut Fourier (1983)

  • Volume: 33, Issue: 4, page 189-201
  • ISSN: 0373-0956

Abstract

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We study one-dimensional oscillator integrals which arise as Fourier-Stieltjes transforms of smooth, compactly supported measures on smooth curves in Euclidean spaces and determine their decay at infinity, provided the curves satisfy certain geometric conditions.

How to cite

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Muller, Detlef. "Estimates of one-dimensional oscillatory integrals." Annales de l'institut Fourier 33.4 (1983): 189-201. <http://eudml.org/doc/74605>.

@article{Muller1983,
abstract = {We study one-dimensional oscillator integrals which arise as Fourier-Stieltjes transforms of smooth, compactly supported measures on smooth curves in Euclidean spaces and determine their decay at infinity, provided the curves satisfy certain geometric conditions.},
author = {Muller, Detlef},
journal = {Annales de l'institut Fourier},
keywords = {one-dimensional oscillatory integrals; smooth, compactly supported measures; smooth curves; decay at infinity},
language = {eng},
number = {4},
pages = {189-201},
publisher = {Association des Annales de l'Institut Fourier},
title = {Estimates of one-dimensional oscillatory integrals},
url = {http://eudml.org/doc/74605},
volume = {33},
year = {1983},
}

TY - JOUR
AU - Muller, Detlef
TI - Estimates of one-dimensional oscillatory integrals
JO - Annales de l'institut Fourier
PY - 1983
PB - Association des Annales de l'Institut Fourier
VL - 33
IS - 4
SP - 189
EP - 201
AB - We study one-dimensional oscillator integrals which arise as Fourier-Stieltjes transforms of smooth, compactly supported measures on smooth curves in Euclidean spaces and determine their decay at infinity, provided the curves satisfy certain geometric conditions.
LA - eng
KW - one-dimensional oscillatory integrals; smooth, compactly supported measures; smooth curves; decay at infinity
UR - http://eudml.org/doc/74605
ER -

References

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  1. [1] F. CARLSON, Une inégalité, Ark. Mat. Astr. Fys., 25, B1 (1934). Zbl0009.34202JFM61.0206.02
  2. [2] L. CORWIN, F. P. GREENLEAF, Singular Fourier integral operators and representations of nilpotent Lie groups, Comm. on Pure and Applied Math., B1 (1978), 681-705. Zbl0391.46033MR81f:46055
  3. [3] Y. DOMAR, On the Banach algebra A(Γ) for smooth sets Γ ⊂Rn, Comment. Math. Helv., 52 (1977), 357-371. Zbl0356.43002MR57 #17121
  4. [4] C. S. HERZ, Fourier transforms related to convex sets, Ann. of Math., (2), 75 (1962), 215-254. Zbl0111.34803MR26 #545
  5. [5] L. HÖRMANDER, Lower bounds at infinity for solutions of differential equations with constant coefficients, Israel J. Math., 16 (1973), 103-116. Zbl0271.35005MR49 #5543
  6. [6] W. LITTMAN, Fourier transforms of surface-carried measures and differentiability of surface averages, Bull, Amer. Math. Soc., 69 (1963), 766-770. Zbl0143.34701MR27 #5086
  7. [7] D. MÜLLER, On the spectral synthesis problem for hypersurfaces of Rn, J. Functional Analysis, 47 (1982), 247-280. Zbl0507.43003

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