On a Kipriyanov problem for a singular ultrahyperbolic equation

2014 ◽  
Vol 50 (4) ◽  
pp. 513-525 ◽  
Author(s):  
L. N. Lyakhov ◽  
I. P. Polovinkin ◽  
E. L. Shishkina
Keyword(s):  
Ultrahyperbolic Equation

Weighted mixed spherical means and singular ultrahyperbolic equation

Analysis ◽  
2016 ◽  
Vol 36 (2) ◽  
Author(s):  
Lev N. Lyakhov ◽  
Elina L. Shishkina
Keyword(s):  
Differential Equation ◽  
Spherical Means ◽  
Spherical Mean ◽  
Euclidian Space ◽  
Ultrahyperbolic Equation ◽  
Generalized Shift

AbstractWeighted mixed spherical means are constructed by using a generalized shift (in a Euclidian space a generalized shift acts with respect to one variable and a usual shift acts with respect to other variables). We obtain the differential equation for weighted mixed spherical mean and prove theorems on weighted mixed spherical means applied to the solution of the B-ultrahyperbolic equation.

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