$\Omega$-ultradistributions

A. V. Abanin

Izvestiya. Mathematics , Tome 72 (2008) no. 2, pp. 207-240.

Résumé

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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