Geodesic
A Fourier-Type Transform on the Semiaxis with an Arbitrary Phase
Matematičeskie zametki, Tome 107 (2020) no. 2, pp. 256-275.

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

Integral equations on the semiaxis with kernels having the form of a linear combination of the Fourier sine and cosine transforms with arbitrary variable complex coefficients are considered. For the case in which the coefficients depend on only one variable, exact solutions are presented. Various generalizations and applications to integral equations are given.
Keywords: integral equations, integral transforms, Fourier transforms, Riemann problem
Mots-clés : Carleman problem. 
@article{MZM_2020_107_2_a8,
     author = {V. \`E. Petrov},
     title = {A {Fourier-Type} {Transform} on the {Semiaxis} with an {Arbitrary} {Phase}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {256--275},
     publisher = {mathdoc},
     volume = {107},
     number = {2},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2020_107_2_a8/}
}
TY  - JOUR
AU  - V. È. Petrov
TI  - A Fourier-Type Transform on the Semiaxis with an Arbitrary Phase
JO  - Matematičeskie zametki
PY  - 2020
SP  - 256
EP  - 275
VL  - 107
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2020_107_2_a8/
LA  - ru
ID  - MZM_2020_107_2_a8
ER  - 
%0 Journal Article
%A V. È. Petrov
%T A Fourier-Type Transform on the Semiaxis with an Arbitrary Phase
%J Matematičeskie zametki
%D 2020
%P 256-275
%V 107
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2020_107_2_a8/
%G ru
%F MZM_2020_107_2_a8
V. È. Petrov. A Fourier-Type Transform on the Semiaxis with an Arbitrary Phase. Matematičeskie zametki, Tome 107 (2020) no. 2, pp. 256-275. http://geodesic.mathdoc.fr/item/MZM_2020_107_2_a8/

[1] G. Beitmen, A. Erdeii, Vysshie transtsendentnye funktsii. Gipergeometricheskaya funktsiya. Funktsii Lezhandra, Nauka, M., 1973 ; Высшие трансцендентные функции. Функции Бесселя, функции параболического цилиндра, ортогональные многочлены, Наука, М., 1974 | MR | Zbl | MR | Zbl

[2] R. C. T. Smith, “An integral equation involving both sine and cosine transforms”, J. Math. Anal. Appl., 48 (1974), 504–514 | DOI | MR | Zbl

[3] W. H. Young, “On infinite integrals involving a generalization of the sine and cosine functions”, Quart. J. Pure Appl. Math., 43 (1912), 161–177 | Zbl

[4] I. Sneddon, Preobrazovaniya Fure, IL, M., 1955 | MR

[5] V. E. Petrov, “Obobschennoe trigonometricheskoe preobrazovanie. Formalnaya teoriya”, Matematicheskie voprosy teorii rasprostraneniya voln. 45, Zap. nauchn. sem. POMI, 438, POMI, SPb., 2015, 203–224 | MR

[6] F. D. Gakhov, Yu. I. Cherskii, Uravneniya tipa svertki, Nauka, M., 1978 | MR | Zbl

[7] F. D. Berkovich, “Ob odnom integralnom uravnenii na poluosi”, Izv. vuzov. Matem., 1966, no. 1, 3–14 | MR | Zbl

[8] F. D. Berkovich, N. V. Govorov, “O kraevoi zadache Karlemana s beskonechnym indeksom”, Sib. matem. zhurn., 12:5 (1971), 1001–1014 | MR | Zbl

[9] I. M. Melnik, “O singulyarnom integro-funktsionalnom uravnenii”, Izv. vuzov. Matem., 1964, no. 2, 100–109 | MR | Zbl

[10] A. P. Prudnikov, Yu. A. Brychkov, Integralnye preobrazovaniya obobschennykh funktsii, Nauka, M., 1977 | MR | Zbl

[11] A. P. Prudnikov, Yu. A. Brychkov, O. I. Marichev, Integraly i ryady. Elementarnye funktsii, Nauka, M., 1981 | MR | Zbl

[12] N. X. Thao, V. A. Kakichev, V. K. Tuan, “On the generalized convolutions for Fourier cosine and sine transforms”, East-West J. Math., 1:1 (1998), 85–90 | MR | Zbl

[13] G. Beitmen, A. Erdeii, V. Magnus, F. Oberkhettinger, F. Trikomi, Tablitsy integralnykh preobrazovanii T. 1. Preobrazovaniya Fure, Laplasa, Mellina, Nauka, M., 1969 | MR | Zbl

[14] F. D. Gakhov, Kraevye zadachi, Nauka, M., 1977 | MR

[15] A. P. Prudnikov, Yu. A. Brychkov, O. I. Marichev, Integraly i ryady. Spetsialnye funktsii, Nauka, M., 1983 | MR