It is shown that the Fourier integral of the function exp(-ux(2)) exists not only for u satisfying Re u gt 0 but also for u that satisfies Re u >= 0. The proof is given by evaluating this integral for imaginary u.
Keywords:
Fourier transform / Cauchy's residue theorem / Fresnel's integrals / wave function behind a grating / interference of matter waves
Source:
Journal of Russian Laser Research, 2006, 27, 3, 220-224
Publisher:
Springer Science and Business Media Deutschland GmbH
TY - JOUR
AU - Davidović, Milena
AU - Božić, Mirjana
AU - Arsenović, Dušan
PY - 2006
UR - http://grafar.grf.bg.ac.rs/handle/123456789/120
AB - It is shown that the Fourier integral of the function exp(-ux(2)) exists not only for u satisfying Re u gt 0 but also for u that satisfies Re u >= 0. The proof is given by evaluating this integral for imaginary u.
PB - Springer Science and Business Media Deutschland GmbH
T2 - Journal of Russian Laser Research
T1 - Evaluation of the fourier transform of e(-ux2) for imaginary U
EP - 224
IS - 3
SP - 220
VL - 27
DO - 10.1007/s10946-006-0010-3
ER -
@article{
author = "Davidović, Milena and Božić, Mirjana and Arsenović, Dušan",
year = "2006",
url = "http://grafar.grf.bg.ac.rs/handle/123456789/120",
abstract = "It is shown that the Fourier integral of the function exp(-ux(2)) exists not only for u satisfying Re u gt 0 but also for u that satisfies Re u >= 0. The proof is given by evaluating this integral for imaginary u.",
publisher = "Springer Science and Business Media Deutschland GmbH",
journal = "Journal of Russian Laser Research",
title = "Evaluation of the fourier transform of e(-ux2) for imaginary U",
pages = "224-220",
number = "3",
volume = "27",
doi = "10.1007/s10946-006-0010-3"
}
Davidović, M., Božić, M.,& Arsenović, D. (2006). Evaluation of the fourier transform of e(-ux2) for imaginary U.
Journal of Russian Laser Research
Springer Science and Business Media Deutschland GmbH., 27(3), 220-224.
https://doi.org/10.1007/s10946-006-0010-3
Davidović M, Božić M, Arsenović D. Evaluation of the fourier transform of e(-ux2) for imaginary U. Journal of Russian Laser Research. 2006;27(3):220-224
Davidović Milena, Božić Mirjana, Arsenović Dušan, "Evaluation of the fourier transform of e(-ux2) for imaginary U" Journal of Russian Laser Research, 27, no. 3 (2006):220-224,
https://doi.org/10.1007/s10946-006-0010-3 .
