The holomorphic functional calculus and infinite dimensional holomorphy

1974 ◽  
pp. 101-108 ◽  
Author(s):  
Lucien Waelbroeck
Keyword(s):  
Functional Calculus ◽  
Holomorphic Functional Calculus ◽  
Infinite Dimensional ◽  
Infinite Dimensional Holomorphy

scholarly journals Bicomplex holomorphic functional calculus

2013 ◽  
Vol 287 (10) ◽  
pp. 1093-1105 ◽  
Author(s):  
Fabrizio Colombo ◽  
Irene Sabadini ◽  
Daniele C. Struppa
Keyword(s):  
Functional Calculus ◽  
Holomorphic Functional Calculus

scholarly journals A SHORT PROOF THAT Mn(A) IS LOCAL IF A IS LOCAL AND FRÉCHET

1992 ◽  
Vol 03 (04) ◽  
pp. 581-589 ◽  
Author(s):  
LARRY B. SCHWEITZER
Keyword(s):  
Banach Algebra ◽  
Functional Calculus ◽  
Short Proof ◽  
Complex Numbers ◽  
Holomorphic Functional Calculus ◽  
General Proof

We give a short and very general proof of the fact that the property of a dense Fréchet subalgebra of a Banach algebra being local, or closed under the holomorphic functional calculus m the Banach algebra, is preserved by tensoring with the n×n matnx algebra of the complex numbers

scholarly journals On non-holomorphic functional calculus for commuting operators

2003 ◽  
Vol 93 (1) ◽  
pp. 109 ◽  
Author(s):  
Sebastian Sandberg
Keyword(s):  
Cohomology Class ◽  
Functional Calculus ◽  
General Scheme ◽  
Holomorphic Functions ◽  
Holomorphic Functional Calculus ◽  
Resolvent Identity ◽  
Commuting Operators

We provide a general scheme to extend Taylor's holomorphic functional calculus for several commuting operators to classes of non-holomorphic functions. These classes of functions will depend on the growth of the operator valued forms that define the resolvent cohomology class. The proofs are based on a generalization of the so-called resolvent identity to several commuting operators.

scholarly journals Application of the functional calculus to solving of infinite dimensional heat equation

2016 ◽  
Vol 8 (2) ◽  
pp. 313-322
Author(s):  
S.V. Sharyn
Keyword(s):  
Cauchy Problem ◽  
Heat Equation ◽  
Functional Calculus ◽  
Ultradifferentiable Functions ◽  
Infinite Dimensional ◽  
Semigroup Approach

In this paper we study infinite dimensional heat equation associated with the Gross Laplacian. Using the functional calculus method, we obtain the solution of appropriate Cauchy problem in the space of polynomial ultradifferentiable functions. The semigroup approach is considered as well.

The holomorphic functional calculus approach to operator semigroups

2013 ◽  
Vol 79 (1-2) ◽  
pp. 289-323
Author(s):  
Charles Batty ◽  
Markus Haase ◽  
Junaid Mubeen
Keyword(s):  
Functional Calculus ◽  
Operator Semigroups ◽  
Holomorphic Functional Calculus
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