Geodesic
$\Omega$-ultradistributions
Izvestiya. Mathematics , Tome 72 (2008) no. 2, pp. 207-240

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We develop a generalization of Beurling's approach to the construction of ultradistribution theory in which Fourier transformation is a basic tool. We establish a structure theorem on the representation of ultradistributions and a theorem of Paley–Wiener–Schwartz type. We illustrate the key role of extending the weights determining the spaces from $N$-dimensional real space, on which they are originally defined, to $N$-dimensional complex space. 
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     author = {A. V. Abanin},
     title = {$\Omega$-ultradistributions},
     journal = {Izvestiya. Mathematics },
     pages = {207--240},
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     volume = {72},
     number = {2},
     year = {2008},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2008_72_2_a0/}
}
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A. V. Abanin. $\Omega$-ultradistributions. Izvestiya. Mathematics , Tome 72 (2008) no. 2, pp. 207-240. http://geodesic.mathdoc.fr/item/IM2_2008_72_2_a0/