@article{SM_1990_67_2_a8,
author = {I. A. Ikromov},
title = {Invariant estimates of two-dimensional trigonometric integrals},
journal = {Sbornik. Mathematics},
pages = {473--488},
year = {1990},
volume = {67},
number = {2},
language = {en},
url = {http://geodesic.mathdoc.fr/item/SM_1990_67_2_a8/}
}
I. A. Ikromov. Invariant estimates of two-dimensional trigonometric integrals. Sbornik. Mathematics, Tome 67 (1990) no. 2, pp. 473-488. http://geodesic.mathdoc.fr/item/SM_1990_67_2_a8/
[1] Airy G. B., “On the intensity of light in the neigbourhood of a caustic”, Trans. Cambridge Philos. Soc., 6 (1838), 379–403
[2] Van der Corput J. G., “Verschartung der Abschatzunder beim Teileproblem”, Math. Ann., 87 (1922), 39–65 | DOI | MR | Zbl
[3] Titchmarch E. C., “The lattice points in a circle”, Proc. Lond. Math. Soc. (2), 38 (1935), 96–115 | DOI
[4] Vinogradov I. M., Metod trigonometricheskikh summ v teorii chisel, Nauka, M., 1980 | MR
[5] Khua Lo-gen, Metod trigonometricheskikh summ i ego primeneniya v teorii chisel, Mir, M., 1964 | MR | Zbl
[6] Min S. H., “On the order $\zeta\bigl(\frac12+it\bigr)$”, Trans. Amer. Math. Soc., 65 (1949), 448–472 | DOI | MR | Zbl
[7] Randol B., “On the Fourier transform of the indicator function of a planar set”, Trans. Amer. Math. Soc., 139 (1969), 271–278 | DOI | MR | Zbl
[8] Randol B., “On the asymptotic behaviour of the Fourier transform of the indicator function of a convex set”, Trans. Amer. Math. Soc., 139 (1969), 279–285 | DOI | MR | Zbl
[9] Duistermaat J., “Oscillatory integrals Lagrange immersions and unifoldings of singularities”, Comm. Pure. Appl. Math., 27:2 (1974), 207–281 | DOI | MR | Zbl
[10] Colin de Verdier Y., Nombre de points entiers dans une famille homothetique de domains de $R^n$, Ann. Scient. Ecole Norm. Super. Ser. 4, 10, 1977 | MR | Zbl
[11] Chubarikov V. N., “O kratnykh ratsionalnykh trigonometricheskikh summakh i kratnykh integralakh”, Matem. zametki, 20:1 (1976), 61–68 | MR | Zbl
[12] Yurinskii V. V., “Otsenki kharakteristicheskikh funktsii nekotorykh vyrozhdennykh mnogomernykh raspredelenii”, Teoriya veroyatnostei i ee primeneniya, 17:1 (1972), 99–110 | MR
[13] Arkhipov G. I., Karatsuba A. A., Chubarikov V. N., “Trigonometricheskie integraly”, Izv. AN SSSR. Ser. matem., 43 (1979), 971–1003 | MR | Zbl
[14] Karpushkin V. N., “Teorema o ravnomernykh otsenkakh ostsilliruyuschikh integralov s fazoi, zavisyaschei ot dvukh peremennykh”, Tr. seminara im. I. G. Petrovskogo, 10 (1983), 3–39 | MR
[15] Bernshtein S. N., Ekstremalnye svoistva polinomov, ONTI, M., L., 1937
[16] Pearcey T., “The structure of an electromagnetic field in the neigbourhood of a cusp of a caustic”, Philos. Mag., 37 (1946), 311–317 | MR
[17] Gurevich G. B., Osnovy teorii algebraicheskikh invariantov, GITL, M., L., 1948 | MR
[18] Malgranzh B., Idealy differentsiruemykh funktsii, Mir, M., 1968
[19] Palamodov V. P., “Deformatsii mnogoobrazii Khopfa i teorema Puankare–Dyulaka”, Funktsion. analiz i ego pril., 17:4 (1983), 7–17 | MR | Zbl
[20] Khadzhiev Dzh., Teoriya invariantov binarnykh form, Fan, Tashkent, 1978 | MR | Zbl
[21] Arnhold J., “Ueber cubische ternäre Formen”, Journ. de Crell., 41 (1850), 25–36
[22] Von Clebsche and Gordan, “Ueber cubische ternäre Formen”, Math. Ann., 6 (1872), 436–512