scholarly journals Division by Flat Ultradifferentiable Functions and Sectorial Extensions

2003 ◽  
Vol 44 (1-2) ◽  
pp. 169-188 ◽  
Author(s):  
Vincent Thilliez
Keyword(s):  
Ultradifferentiable Functions

scholarly journals Nuclear global spaces of ultradifferentiable functions in the matrix weighted setting

2020 ◽  
Vol 15 (1) ◽  
Author(s):  
Chiara Boiti ◽  
David Jornet ◽  
Alessandro Oliaro ◽  
Gerhard Schindl
Keyword(s):  
Hermite Functions ◽  
Weighted Spaces ◽  
Schauder Basis ◽  
Weight Functions ◽  
Ultradifferentiable Functions ◽  
The Matrix ◽  
General Conditions

AbstractWe prove that the Hermite functions are an absolute Schauder basis for many global weighted spaces of ultradifferentiable functions in the matrix weighted setting and we determine also the corresponding coefficient spaces, thus extending the previous work by Langenbruch. As a consequence, we give very general conditions for these spaces to be nuclear. In particular, we obtain the corresponding results for spaces defined by weight functions.

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