Geodesic
Fourier Integrals, Special Functions, and the Semicontinuity Phenomenon
Funkcionalʹnyj analiz i ego priloženiâ, Tome 35 (2001) no. 2, pp. 53-63 
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/
@article{FAA_2001_35_2_a4,
     author = {V. P. Palamodov},
     title = {Fourier {Integrals,} {Special} {Functions,} and the {Semicontinuity} {Phenomenon}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
     pages = {53--63},
     year = {2001},
     volume = {35},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2001_35_2_a4/}
}
TY  - JOUR
AU  - V. P. Palamodov
TI  - Fourier Integrals, Special Functions, and the Semicontinuity Phenomenon
JO  - Funkcionalʹnyj analiz i ego priloženiâ
PY  - 2001
SP  - 53
EP  - 63
VL  - 35
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/FAA_2001_35_2_a4/
LA  - ru
ID  - FAA_2001_35_2_a4
ER  - 
%0 Journal Article
%A V. P. Palamodov
%T Fourier Integrals, Special Functions, and the Semicontinuity Phenomenon
%J Funkcionalʹnyj analiz i ego priloženiâ
%D 2001
%P 53-63
%V 35
%N 2
%U http://geodesic.mathdoc.fr/item/FAA_2001_35_2_a4/
%G ru
%F FAA_2001_35_2_a4

Voir la notice de l'article provenant de la source Math-Net.Ru

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.

[1] Arnold V. I., Gusein-Zade S. M., Varchenko A. N., Osobennosti differentsiruemykh otobrazhenii, T. 1, Nauka, M., 1982 | MR

[2] Hörmander L., “Fourier integral operators, I”, Acta Math., 127:1–2 (1971), 79–183 | DOI | MR | Zbl

[3] Palamodov V. P., “Asimptoticheskie razlozheniya integralov v kompleksnoi i veschestvennoi oblastyakh”, Matem. sb., 127:2 (1985), 209–238 | MR | Zbl

[4] Palamodov V. P., Obobschennye funktsii i garmonicheskii analiz, 72, VINITI, 1991 | MR

[5] Palamodov V. P., “Special functions of several variables”, Linear topological spaces and complex analysis III. METU-Tubitak (Ankara, 1997), 120–137 | MR | Zbl

[6] Palamodov V. P., “Dynamics of wave propagation and curvature of discriminants”, Ann. Inst. Fourier, 50:6 (2000), 1945–1981 | DOI | MR | Zbl

[7] Saito K., “Quasihomogene isolierte Singularitäten von Hyperflächen”, Invent. Math., 14 (1971), 123–142 | DOI | MR | Zbl