Estimates for the Fourier Transform of the Indicator Function for Nonconvex Domains
Funkcionalʹnyj analiz i ego priloženiâ, Tome 29 (1995) no. 3, pp. 16-24.

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

@article{FAA_1995_29_3_a1,
     author = {I. A. Ikromov},
     title = {Estimates for the {Fourier} {Transform} of the {Indicator} {Function} for {Nonconvex} {Domains}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
     pages = {16--24},
     publisher = {mathdoc},
     volume = {29},
     number = {3},
     year = {1995},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_1995_29_3_a1/}
}
TY  - JOUR
AU  - I. A. Ikromov
TI  - Estimates for the Fourier Transform of the Indicator Function for Nonconvex Domains
JO  - Funkcionalʹnyj analiz i ego priloženiâ
PY  - 1995
SP  - 16
EP  - 24
VL  - 29
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/FAA_1995_29_3_a1/
LA  - ru
ID  - FAA_1995_29_3_a1
ER  - 
%0 Journal Article
%A I. A. Ikromov
%T Estimates for the Fourier Transform of the Indicator Function for Nonconvex Domains
%J Funkcionalʹnyj analiz i ego priloženiâ
%D 1995
%P 16-24
%V 29
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/FAA_1995_29_3_a1/
%G ru
%F FAA_1995_29_3_a1
I. A. Ikromov. Estimates for the Fourier Transform of the Indicator Function for Nonconvex Domains. Funkcionalʹnyj analiz i ego priloženiâ, Tome 29 (1995) no. 3, pp. 16-24. http://geodesic.mathdoc.fr/item/FAA_1995_29_3_a1/

[1] Herz C. S., “Fourier transforms related to convex set”, Ann. Math., 75:2 (1962), 215–254 | MR

[2] Randol B., “On the Fourier transform of the indicator function of a planar set”, Trans. Am. Math. Soc., 139 (1969), 271–278 | DOI | MR | Zbl

[3] Randol B., “On the asymptotic behaviour of the Fourier transform of the indicator function of a convex set”, Trans. Am. Math. Soc., 139 (1969), 278–285 | MR

[4] Svensson I., “Estimates for the Fourier transform of the characteristic function of a convex set”, Ark. Mat., 9:1 (1970), 11–22 | DOI | MR

[5] Colin de Verdier Y., “Nombre de points entiers dans une famille homothetique de domains de $\mathbb R^n$”, Ann. Sci. École Norm. Sup. (4), 10:4 (1977), 559–575 | DOI | MR

[6] Varchenko A. N., “O chisle tselykh tochek v semeistvakh gomotetichnykh oblastei”, Funkts. analiz i ego pril., 17:2 (1983), 1–6 | MR | Zbl

[7] Arnold V. I., Varchenko A. N., Gusein-Zade S. M., Osobennosti differentsiruemykh otobrazhenii. Klassifikatsiya kriticheskikh tochek, kaustik i volnovykh frontov, Nauka, M., 1982 | MR

[8] Malgranzh B., Idealy differentsiruemykh funktsii, Mir, M., 1968

[9] Duistermaat J., “Oscillatory integrals, Lagrange immersions and unifoldings of singularities”, Comm. Pure Appl. Math., 27:2 (1974), 207–281 | DOI | MR | Zbl

[10] Mazer Dzh., “Strukturnaya ustoichivost otobrazhenii”, Osobennosti differentsiruemykh otobrazhenii, Mir, M., 1968, 216–267

[11] Karpushkin V. N., “Ravnomernye otsenki ostsilliruyuschikh integralov s parabolicheskoi ili giperbolicheskoi fazoi”, Trudy seminara im. I. G. Petrovskogo, 9, 1983, 3–39 | MR | Zbl

[12] Arnold V. I., “Osobennosti gladkikh otobrazhenii”, UMN, 23:1 (1968), 3–44 | MR

[13] Arnold V. I., “Normalnye formy funktsii vblizi vyrozhdennykh kriticheskikh tochek, gruppy Veilya $A_k$, $D_k$, $E_k$ i lagranzhevy osobennosti”, Funkts. analiz i ego pril., 6:4 (1972), 3–25 | DOI | MR

[14] Kolmogorov A. N., Fomin S. V., Elementy teorii funktsii i funktsionalnogo analiza, Nauka, M., 1989 | MR

[15] Ikromov I. A., “Invariantnye otsenki dvumernykh trigonometricheskikh integralov”, Matem. sb., 180:8 (1989), 1017–1032