Geodesic
Asymptotic behavior of the two-point Wightman function
Teoretičeskaâ i matematičeskaâ fizika, Tome 40 (1979) no. 1, pp. 28-37 
K. A. Bukin. Asymptotic behavior of the two-point Wightman function. Teoretičeskaâ i matematičeskaâ fizika, Tome 40 (1979) no. 1, pp. 28-37. http://geodesic.mathdoc.fr/item/TMF_1979_40_1_a2/
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     title = {Asymptotic behavior of the two-point {Wightman} function},
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     url = {http://geodesic.mathdoc.fr/item/TMF_1979_40_1_a2/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

It is shown that there is a one-to-one correspondence between the quasiasymptotic behavior of the two-point Wightman function in the $p$ representation and the asymptotic behavior of the Fourier transform in the neighborhood of the light cone. As a consequence, the modified Tauber theorem of Vladimirov is used to obtain an assertion about the connection between the asymptotic behavior of the antiderivative of the two-point function at infinity and the behavior of the Laplace transform in the neighborhood of the origin.

[1] V. S. Vladimirov, Obobschennye funktsii v matematicheskoi fizike, «Nauka», 1976 | MR | Zbl

[2] V. S. Vladimirov, Metody teorii funktsii mnogikh kompleksnykh peremennykh, «Nauka», 1964 | MR

[3] V. S. Vladimirov, Izv. AN SSSR, ser. matem., 40 (1976), 1084 | MR | Zbl

[4] B. I. Zavyalov, TMF, 17 (1973), 178

[5] P. D. Methée, Commun. Math. Helv., 28 (1954), 225 | DOI | MR | Zbl

[6] I. M. Gelfand, G. E. Shilov, Obobschennye funktsii, vyp. 1, Fizmatgiz, 1958 | MR

[7] K. A. Bukin, Tr. MFTI, Radiotekhnika i elektronika, Dolgoprudnyi, 1977, 92

[8] Yu. N. Drozhzhinov, B. I. Zavyalov, Mat. sb., 108(150):1 (1979), 78–90 | MR | Zbl