Permutability of cosine and sine Fourier transforms
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 2 (2019), pp. 46-49 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

It is proved that the cosine and sine Fourier transforms are permutable with the opposite sign on the positive real axis. This property implies that the cosine and sine Fourier transforms coincide in absolute value on the semiaxis for a wide class of functions.
@article{VMUMM_2019_2_a8,
     author = {A. V. Pavlov},
     title = {Permutability of cosine and sine {Fourier} transforms},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {46--49},
     year = {2019},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2019_2_a8/}
}
TY  - JOUR
AU  - A. V. Pavlov
TI  - Permutability of cosine and sine Fourier transforms
JO  - Vestnik Moskovskogo universiteta. Matematika, mehanika
PY  - 2019
SP  - 46
EP  - 49
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/VMUMM_2019_2_a8/
LA  - ru
ID  - VMUMM_2019_2_a8
ER  - 
%0 Journal Article
%A A. V. Pavlov
%T Permutability of cosine and sine Fourier transforms
%J Vestnik Moskovskogo universiteta. Matematika, mehanika
%D 2019
%P 46-49
%N 2
%U http://geodesic.mathdoc.fr/item/VMUMM_2019_2_a8/
%G ru
%F VMUMM_2019_2_a8
A. V. Pavlov. Permutability of cosine and sine Fourier transforms. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 2 (2019), pp. 46-49. http://geodesic.mathdoc.fr/item/VMUMM_2019_2_a8/

[1] Pavlov A. V., Distsipliny s prioritetom korotkim trebovaniyam i identichnoe obsluzhivanie, FGBOU VPO MGTU MIREA, M., 2013 http://catalog.inforeg.ru/Inet/GetEzineByID/300386

[2] Kolmogorov A. N., Fomin S. V., Elementy teorii funktsii i funktsionalnogo analiza, Nauka, M., 1976 | MR

[3] Pavlov A. V., “The Dirichlet problem and disappearance of the imaginary part of the Laplace transform on the imaginary axis in connection with the Fourier, Laplace operators”, The 8th Int. Conf. on Differential and Functional Differential Equations (August 13–20, 2017, Moscow, RUDN Univ., Steklov Math. Inst.), M., 2017, 137

[4] Pavlov A. V., “Identical service and the odd or even transform of Laplace”, Conf. “Anal. and comp. meth. in probab. theor. and its appl” (ACMPT 2017) (October 23–27, 2017, Moscow, Moscow M. V. Lomonosov Univ., RUDN), M., 2017, 31–35

[5] Pavlov A. V., “The correctness of geometrical methods in the theorem of Fermat; the transform of Laplace”, 7th Eur. Congr. Math. (July 18–22, 2016, Techn. Univers. Berlin), 84

[6] Pavlov A. V., “Application of regularity of the double Laplace transform to the general properties of the integral Fourier transform”, Int. Conf. “Math. theory of optimal control”. Proc. Int. Conf. dedicated to the 90th universary of Acad. R. V. Gamkrelidze (June 1–2, 2017, Moscow, Steklov. Math. Inst. (KSA Innov. Group)), M., 2017, 113–115

[7] Pavlov A. V., “Preobrazovanie Fure i formula obrascheniya preobrazovaniya Laplasa”, Matem. zametki, 90:6 (2011), 792–796

[8] Pavlov A. V., “About the equality of the transform of Laplace to the transform of Fourier”, Issues of Analysis. Petrozavodsk, 23:1 (2016), 21–30 | DOI | MR | Zbl

[9] Arkhipov G. I., Chubarikov V. N., “O matematicheskikh rabotakh professora A. A. Karatsuby”, Analiticheskaya teoriya chisel i prilozheniya, Sbornik statei. K 60-letiyu so dnya rozhdeniya professora Anatoliya Alekseevicha Karatsuby, Tr. MIAN, 218, 1997, 7–19 | MR | Zbl

[10] Lykov A. A., Malyshev V. A., Chubarikov V. N., “Regulyarnye kontinualnye sistemy tochechnykh chastits. I: Sistemy bez vzaimodeistviya”, Chebyshevskii sbornik, 17:3 (2016), 148–165 | DOI | MR

[11] Pavlov A. V., “Dostovernoe prognozirovanie funktsii, predstavimykh v vide preobrazovaniya Fure ili Laplasa”, Vestn. MGTU MIREA, 3:2 (2014), 78–85

[12] Lavrentev M. A., Shabat B. V., Metody teorii funktsii kompleksnogo peremennogo, Nauka, M., 1987

[13] Fikhtengolts G. M., Kurs differentsialnogo i integralnogo ischisleniya, v. II, Nauka, M., 1969