Boson star solutions of the Einstein-Klein-Gordon equations in the sense of Colombeau-Egorov's theory of generalized functions

2017 ◽  
Vol 338 (9-10) ◽  
pp. 1094-1100
Author(s):  
A. Cabo Montes de Oca ◽  
D. Suárez Fontanella ◽  
N. G. Cabo Bizet
Keyword(s):  
Generalized Functions ◽  
Klein Gordon ◽  
Theory Of Generalized Functions

scholarly journals A remark on convergence of test functions

1975 ◽  
Vol 20 (1) ◽  
pp. 73-76 ◽  
Author(s):  
W. F. Moss
Keyword(s):  
Uniform Convergence ◽  
Pointwise Convergence ◽  
Generalized Functions ◽  
Test Functions ◽  
Definition Of ◽  
Theory Of Generalized Functions

In this note it is shown in the most frequently encountered spaces of test functions in the theory of generalized functions that the customary definitions of convergence are equivalent to apparently much weaker definitions. For example, in the space g the condition of uniform convergence of the functions together with all derivatives (which appears in the definition of convergence) is equivalent to the condition of pointwise convergence of the functions alone. Thus verification of convergence is simplified somewhat.

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