Geodesic
Fourier Integrals, Special Functions, and the Semicontinuity Phenomenon
Funkcionalʹnyj analiz i ego priloženiâ, Tome 35 (2001) no. 2, pp. 53-63

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For a real weighted homogeneous hypersurface germ, we consider elliptic deformations and related special functions. Singularities of these special functions are characterized by some rational numbers called energy exponents. We apply the residue mapping to the corresponding Fourier integrals and give a geometric interpretation of the energy exponents in the terms of the volume of the associated Lagrangian manifold. The energy exponents are calculated for a series of examples. Two conjectures concerning the energy exponents are discussed. 
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     author = {V. P. Palamodov},
     title = {Fourier {Integrals,} {Special} {Functions,} and the {Semicontinuity} {Phenomenon}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
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     number = {2},
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     url = {http://geodesic.mathdoc.fr/item/FAA_2001_35_2_a4/}
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V. P. Palamodov. Fourier Integrals, Special Functions, and the Semicontinuity Phenomenon. Funkcionalʹnyj analiz i ego priloženiâ, Tome 35 (2001) no. 2, pp. 53-63. http://geodesic.mathdoc.fr/item/FAA_2001_35_2_a4/