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.

Spherical Mean and the Fundamental Group

1991 ◽  
Vol 34 (1) ◽  
pp. 3-11 ◽  
Author(s):  
Toshiaki Adachi
Keyword(s):  
Riemannian Manifold ◽  
Fundamental Group ◽  
Random Walks ◽  
Isoperimetric Inequality ◽  
Lower Bounds ◽  
Compact Riemannian Manifold ◽  
Universal Covering ◽  
Spherical Means ◽  
Universal Covering Space ◽  
Spherical Mean

AbstractWe investigate some properties of spherical means on the universal covering space of a compact Riemannian manifold. If the fundamental group is amenable then the greatest lower bounds of the spectrum of spherical Laplacians are equal to zero. If the fundamental group is nontransient so are geodesic random walks. We also give an isoperimetric inequality for spherical means.

Eigenvalue Problem for the Second Order Differential Equation with Nonlocal

2006 ◽  
Vol 11 (1) ◽  
pp. 13-32 ◽  
Author(s):  
B. Bandyrskii ◽  
I. Lazurchak ◽  
V. Makarov ◽  
M. Sapagovas
Keyword(s):  
Differential Equation ◽  
Eigenvalue Problem ◽  
Variable Coefficient ◽  
Order Differential Equation ◽  
Integral Condition ◽  
Second Order ◽  
Computational Results ◽  
Discrete Method ◽  
Complex Eigenvalues ◽  
Nonlocal Integral Condition

The paper deals with numerical methods for eigenvalue problem for the second order ordinary differential operator with variable coefficient subject to nonlocal integral condition. FD-method (functional-discrete method) is derived and analyzed for calculating of eigenvalues, particulary complex eigenvalues. The convergence of FD-method is proved. Finally numerical procedures are suggested and computational results are schown.

Fuzzy Euler differential equation

2015 ◽  
Vol 2 (1) ◽  
pp. 1-12 ◽  
Author(s):  
S. Melliani ◽  
◽  
L. Chadli ◽  
A. Harir
Keyword(s):  
Differential Equation
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