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- W1996752907 abstract "In [A.G. Smirnov, Fourier transformation of Sato's hyperfunctions, Adv. Math. 196 (2005) 310–345] the author introduced a new generalized function space U(Rk) which can be naturally interpreted as the Fourier transform of the space of Sato's hyperfunctions on Rk. It was shown that all Gelfand–Shilov spaces Sα′0(Rk) (α>1) of analytic functionals are canonically embedded in U(Rk). While the usual definition of support of a generalized function is inapplicable to elements of Sα′0(Rk) and U(Rk), their localization properties can be consistently described using the concept of carrier cone introduced by Soloviev [M.A. Soloviev, Towards a generalized distribution formalism for gauge quantum fields, Lett. Math. Phys. 33 (1995) 49–59; M.A. Soloviev, An extension of distribution theory and of the Paley–Wiener–Schwartz theorem related to quantum gauge theory, Comm. Math. Phys. 184 (1997) 579–596]. In this paper, the relation between carrier cones of elements of Sα′0(Rk) and U(Rk) is studied. It is proved that an analytic functional u∈Sα′0(Rk) is carried by a cone K⊂Rk if and only if its canonical image in U(Rk) is carried by K." @default.
- W1996752907 created "2016-06-24" @default.
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- W1996752907 date "2009-03-01" @default.
- W1996752907 modified "2023-09-26" @default.
- W1996752907 title "On localization properties of Fourier transforms of hyperfunctions" @default.
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- W1996752907 doi "https://doi.org/10.1016/j.jmaa.2008.10.003" @default.
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