neutrix product
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2014 ◽  
Vol 07 (03) ◽  
pp. 1450042
Author(s):  
Mongkolsery Lin ◽  
Somsak Orankitjaroen ◽  
Brian Fisher

In distribution theory, the product of two distributions can only be defined under certain conditions. In this paper, by using Fisher's definition, it is proved that if Gm,s(x) denotes the distribution ( ln m+1x-)(s), then the noncommutative neutrix product [Formula: see text] exists and [Formula: see text] for m, s ≥ 1, where [Formula: see text]. Related neutrix products are then deduced.



2009 ◽  
Vol 20 (1) ◽  
pp. 35-44 ◽  
Author(s):  
Brian Fisher ◽  
Kenan Taş
Keyword(s):  






2007 ◽  
Vol 2007 ◽  
pp. 1-10
Author(s):  
Emin Özçaḡ ◽  
İnci Ege ◽  
Haşmet Gürçay ◽  
Biljana Jolevska-Tuneska

Letfandgbe distributions and letgn=(g*δn)(x), whereδn(x)is a certain sequence converging to the Dirac-delta functionδ(x). The noncommutative neutrix productf∘goffandgis defined to be the neutrix limit of the sequence{fgn}, provided the limithexists in the sense thatN‐limn→∞〈f(x)gn(x),φ(x)〉=〈h(x),φ(x)〉, for all test functions in𝒟. In this paper, using the concept of the neutrix limit due to van der Corput (1960), the noncommutative neutrix productsx+rlnx+∘x−−r−1lnx−andx−−r−1lnx−∘x+rlnx+are proved to exist and are evaluated forr=1,2,…. It is consequently seen that these two products are in fact equal.



2006 ◽  
Vol 17 (7) ◽  
pp. 513-519 ◽  
Author(s):  
Brian Fisher ◽  
Kenan Taş
Keyword(s):  




2005 ◽  
Vol 16 (2) ◽  
pp. 131-138 ◽  
Author(s):  
Brian Fisher ◽  
Kenan Taş
Keyword(s):  


2001 ◽  
Vol 11 (1) ◽  
pp. 49-60 ◽  
Author(s):  
E. Özça[Gbar] ◽  
B. Fisher ◽  
H. Gürçay
Keyword(s):  


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