Evaluation of the fourier transform of e(-ux2) for imaginary U
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.
Keywords:
Fourier transform / Cauchy's residue theorem / Fresnel's integrals / wave function behind a grating / interference of matter wavesSource:
Journal of Russian Laser Research, 2006, 27, 3, 220-224Publisher:
- Springer Science and Business Media Deutschland GmbH
Projects:
- Govorna komunikacija čovek-mašina (RS-11001)
DOI: 10.1007/s10946-006-0010-3
ISSN: 1071-2836
WoS: 000241073100003
Scopus: 2-s2.0-33747043093
Collections
Institution
GraFarTY - 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. Evaluation of the fourier transform of e(-ux2) for imaginary U. Journal of Russian Laser Research. 2006;27(3):220-224
Davidović, M., Božić, M.,& Arsenović, D. (2006). Evaluation of the fourier transform of e(-ux2) for imaginary U. Journal of Russian Laser ResearchSpringer Science and Business Media Deutschland GmbH., 27(3), 220-224. https://doi.org/10.1007/s10946-006-0010-3
Davidović Milena, Božić Mirjana, Arsenović Dušan, "Evaluation of the fourier transform of e(-ux2) for imaginary U" 27, no. 3 (2006):220-224, https://doi.org/10.1007/s10946-006-0010-3 .