JournalspmVol. 65 , No. 2pp. 285–309

The Fourier–Borel transform between spaces of entire functions of a given type and order

  • Vinícius Vieira Fávaro

    Universidade Federal de Uberlândia, Brazil
The Fourier–Borel transform between spaces of entire functions of a given type and order cover
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Abstract

In this article we study the Fourier–Borel transform between the dual of ExpkÑ,(s;( r,q)),A(E), the space of entire functions on E of (s;(r,q))-quasi-nuclear order k and (s;(r,q))-quasi-nuclear type strictly less than A, and the space Expk'(s',m(r';q')),0,(θ(k)A)−1(E') of entire functions on E' of (s',m(r';q'))-summing order k and (s',m(r';q'))-summing type less than or equal to (θ(k)A)−1. This mapping identifies algebraically and topologically these two spaces. On the dual space it is considered the strong topology. This generalizes results of Matos [4] and Martineau [3].

Cite this article

Vinícius Vieira Fávaro, The Fourier–Borel transform between spaces of entire functions of a given type and order. Port. Math. 65 (2008), no. 2 pp. 285–309

DOI 10.4171/PM/1813