scholarly journals Square integrable holomorphic functions on infinite-dimensional Heisenberg type groups

2009 ◽  
Vol 147 (3-4) ◽  
pp. 481-528 ◽  
Author(s):  
Bruce K. Driver ◽  
Maria Gordina
Keyword(s):  
Holomorphic Functions ◽  
Infinite Dimensional ◽  
Heisenberg Type ◽  
Heisenberg Type Groups

Holomorphic functions with distinguished properties on infinite dimensional spaces

2018 ◽  
Vol 70 (3) ◽  
pp. 797-811
Author(s):  
Thiago R Alves ◽  
Geraldo Botelho
Keyword(s):  
Banach Space ◽  
Holomorphic Functions ◽  
Complex Banach Space ◽  
Algebraic Structures ◽  
Infinite Dimensional ◽  
Zero Function ◽  
Bounded Holomorphic

Abstract In this paper, we develop a method to construct holomorphic functions that exist only on infinite dimensional spaces. The following types of holomorphic functions f:U→ℂ on some open subsets U of an infinite dimensional complex Banach space are constructed: (1) f is bounded holomorphic on U and is continuously, but not uniformly continuously extended to U¯; (2) f is continuous on U¯ and holomorphic of bounded type on U, but f is unbounded on U; (3) f is holomorphic of bounded type on U and f cannot be continuously extended to U¯. The technique we develop is powerful enough to provide, in the cases (2) and (3) above, large algebraic structures formed by such functions (up to the zero function, of course).

scholarly journals ON THE ANNIHILATOR OF A DOLBEAULT GROUP

2010 ◽  
Vol 21 (03) ◽  
pp. 317-331
Author(s):  
IMRE PATYI
Keyword(s):  
Holomorphic Function ◽  
Open Subset ◽  
Cohomology Group ◽  
Holomorphic Functions ◽  
Dolbeault Cohomology ◽  
Infinite Dimensional ◽  
Continuous Character

We show that any Dolbeault cohomology group Hp,q(D), p ≥ 0, q ≥ 1, of an open subset D of a closed finite codimensional complex Hilbert submanifold of ℓ2 is either zero or infinite dimensional. We also show that any continuous character of the algebra of holomorphic functions of a closed complex Hilbert submanifold M of ℓ2 is induced by its evaluation at a point of M. Lastly, we prove that any closed split infinite dimensional complex Banach submanifold of ℓ2 admits a nowhere critical holomorphic function.

Marcinkiewicz multipliers and multi-parameter structure on Heisenberg (-type) groups, I

1995 ◽  
Vol 119 (1) ◽  
pp. 199-233 ◽  
Author(s):  
Detlef M�ller ◽  
Fulvio Ricci ◽  
Elias M. Stein
Keyword(s):  
Heisenberg Type ◽  
Heisenberg Type Groups ◽  
Marcinkiewicz Multipliers
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