holomorphy types
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2018 ◽  
Vol 468 (2) ◽  
pp. 622-641
Author(s):  
Santiago Muro ◽  
Damián Pinasco ◽  
Martín Savransky


2012 ◽  
Vol 110 (1) ◽  
pp. 111 ◽  
Author(s):  
Vinícius V. Fávaro ◽  
Ariosvaldo M. Jatobá

Let $E$ be a Banach space and $\Theta$ be a $\pi_{1}$-holomorphy type. The main purpose of this paper is to show that the Fourier-Borel transform is an algebraic isomorphism between the dual of the space ${\operatorname{Exp}}_{\Theta,A}^{k}(E)$ of entire functions on $E$ of order $k$ and $\Theta$-type strictly less than $A$ and the space ${\operatorname{Exp}}_{\Theta^{\prime},0,(\lambda (k) A)^{-1}}^{k^{\prime}}(E^{\prime})$ of entire functions on $E^{\prime}$ of order $k^{\prime}$ and $\Theta^{\prime}$-type less than or equal to $(\lambda(k)A)^{-1}$. The same is proved for the dual of the space ${\operatorname{Exp}}_{\Theta,A}^{k}(E)$ of entire functions on $E$ of order $k$ and $\Theta$-type less than or equal to $A$ and the space ${\operatorname{Exp}}_{\Theta^{\prime}, (\lambda(k)A)^{-1}}^{k^{\prime}}( E^{\prime})$ of entire functions on $E^{\prime}$ of order $k^{\prime}$ and $\Theta^{\prime}$-type strictly less than $(\lambda(k)A)^{-1}$. Moreover, the Fourier-Borel transform is proved to be a topological isomorphism in certain cases.



2009 ◽  
Vol 59 (4) ◽  
pp. 909-927 ◽  
Author(s):  
Vinícius V. Fávaro ◽  
Ariosvaldo M. Jatobá


2006 ◽  
Vol 177 (1) ◽  
pp. 43-65 ◽  
Author(s):  
G. Botelho ◽  
H.-A. Braunss ◽  
H. Junek ◽  
D. Pellegrino


Author(s):  
Mário C. Matos ◽  
Leopoldo Nachbin
Keyword(s):  


1973 ◽  
Vol 45 (3) ◽  
pp. 273-289 ◽  
Author(s):  
Richard Aron


1971 ◽  
Vol 39 (3) ◽  
pp. 241-288 ◽  
Author(s):  
Seán Dineen


1970 ◽  
Vol 38 (1) ◽  
pp. 407-412 ◽  
Author(s):  
Leopoldo Nachbin




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