The Fourier Transforms of Smooth Measures on Hypersurfaces of Rn + 1
1986 ◽
Vol 38
(2)
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pp. 328-359
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Keyword(s):
The Fourier transform of the surface measure on the unit sphere in Rn + 1, as is well-known, equals the Bessel functionIts behaviour at infinity is described by an asymptotic expansionThe purpose of this paper is to obtain such an expression for surfaces Σ other than the unit sphere. If the surface Σ is a sufficiently smooth compact n-surface in Rn + 1 with strictly positive Gaussian curvature everywhere then with only minor changes in the main term, such an asymptotic expansion exists. This result was proved by E. Hlawka in [3]. A similar result concerned with the minimal smoothness of Σ was later obtained by C. Herz [2].
1965 ◽
Vol 5
(3)
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pp. 289-298
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Keyword(s):
1979 ◽
Vol 31
(6)
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pp. 1281-1292
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1992 ◽
Vol 436
(1896)
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pp. 109-120
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1936 ◽
Vol 32
(2)
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pp. 321-327
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Keyword(s):
1992 ◽
Vol 111
(3)
◽
pp. 525-529
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1941 ◽
Vol 37
(4)
◽
pp. 331-348
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1984 ◽
Vol 36
(4)
◽
pp. 685-717
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