Holographic Reduction: A Domain Changed Application and Its Partial Converse Theorems

2010 ◽  
pp. 666-677 ◽  
Author(s):  
Mingji Xia
Keyword(s):  
Converse Theorems ◽  
Partial Converse

Characterizations of the normal distribution by suitable transformations

1973 ◽  
Vol 10 (1) ◽  
pp. 100-108 ◽  
Author(s):  
S. Beer ◽  
E. Lukacs
Keyword(s):  
Sample Size ◽  
Normal Distribution ◽  
Functional Equations ◽  
Normal Sample ◽  
Population Mean ◽  
Converse Theorems

Yu. V. Linnik showed that certain transformations, given by Formulae (1.1), (1.6) and (1.7) transform a normal sample into itself. The transformations (1.1) and (1.7) apply to samples of size 2 while (1.6) admits an arbitrary sample size. It is also assumed that the population mean is zero.In the present paper the converse theorems are proven so that characterizations of the normal distribution are obtained. The problem leads to the functional equations (2.3) and (2.13) whose solution yields the desired results.

Direct and strong converse theorems for a general sequence of positive linear operators

2012 ◽  
Vol 136 (1-2) ◽  
pp. 90-106 ◽  
Author(s):  
Jorge Bustamante ◽  
Abisaí Carrillo-Zentella ◽  
José M. Quesada
Keyword(s):  
Linear Operators ◽  
Positive Linear Operators ◽  
General Sequence ◽  
Converse Theorems ◽  
Strong Converse
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