References
- Dym H, McKean HP. Fourier series and integrals. New York: Academic Press; 1972.
- Hörmander L. A uniqueness theorem of Beurling for Fourier transform pairs. Ark Mat. 1991;29:237–240. doi: https://doi.org/10.1007/BF02384339
- Sitaram A, Sundari M, Thangavelu S. Uncertainty principles on certain Lie groups. Proc Indian Acad Sci (Math Sci). 1995;105(2):135–151. doi: https://doi.org/10.1007/BF02880360
- Armitage DH. Uniqueness theorems for harmonic functions in domains of revolution. J London Math Soc. 1977;15(2):103–112. doi: https://doi.org/10.1112/jlms/s2-15.1.103
- Armitage DH. Uniqueness theorems for harmonic functions in half-space. J Math Anal Appl. 1985;106:219–236. doi: https://doi.org/10.1016/0022-247X(85)90145-3
- Carlson F. Sur une classe de séries de Talor [thesis]. Upsala: 1914.
- Aršon IS, Par MA. A uniqueness theorem for harmonic functions in a half-space. Mat Sb (NS). 1965;68:148–151. [Russian].
- Armitage DH. A new proof of a uniqueness theorems for harmonic functions in half-space. Bull London Math Soc. 1977;9:317–320. doi: https://doi.org/10.1112/blms/9.3.317
- Dzhrbashyan MM. Uniqueness theorems for Fourier transforms and for infinity differentiable functions. Izv Akad Nauk Armyan SSr Ser Mat. 1957;10(6):7–24.
- Levi BY. Lectures on entire functions. Providence (RI): American Mathematical Society; 1996.
- Lev N. Uniqueness theorems for Fourier transform. Bull Sci Math. 2011;135:134–140. doi: https://doi.org/10.1016/j.bulsci.2010.12.002
- Zhang YH, Deng GT, Kou KI. On the lower bound for a class of harmonic functions in the half-space. Acta Math Sci (Ser B). 2012;32B(4):1487–1494.
- Bray WO, Pinsky MA. Growth properties of Fourier transform via modui of continuity. J Funct Anal. 2009;255:2265–2285. doi: https://doi.org/10.1016/j.jfa.2008.06.017
- Bray WO, Pinsky MA. Growth properties of the Fourier transform. Filomat. 2012;26(4):755–760. doi: https://doi.org/10.2298/FIL1204755B
- Bray WO. Growth and integrability of Fourier transforms on Euclidean space. J Fourier Anal Appl. 2014;20(6):1234–1256. doi: https://doi.org/10.1007/s00041-014-9354-1
- Bonali A, Demange B, Jaming P. Hermite functions and uncertainty principles for the Fourier and the windowed Fourier transforms. Rev Mat Iheroam. 2003;1(19):23–55.
- Boas RP. Entire functions. New York: Academic Press; 1954.
- Zhang YH. Phrágmen-Lindelóf theorems of subharmonic functions and their applications in the half-space. Sci Sin Math. 2015;45(12):1931–1938. Chinese. doi: https://doi.org/10.1360/N012014-00198
- Zhang YH, Deng GT, Kou KI. Asymptotic behavior of fractional Laplacians in the half space. Appl Math Comput. 2015;254:125–132.
- Gelfand IM, Shilov GE. Generalized functions II. Spaces of fundamental and generalized functions. New York: Academic Press; 1968.