Beamforming with Higher-Order Linear Difference Equations

2021 ◽  
pp. 109-140
Author(s):  
Jacob Benesty ◽  
Israel Cohen ◽  
Jingdong Chen
Keyword(s):  
Difference Equations ◽  
Higher Order ◽  
Linear Difference Equations ◽  
Order Linear

Asymptotic behavior of a system of higher order linear difference equations

2001 ◽  
Vol 47 (7) ◽  
pp. 4667-4677 ◽  
Author(s):  
Hideaki Matsunaga ◽  
Ryuzou Ogita ◽  
Kouichi Murakami
Keyword(s):  
Asymptotic Behavior ◽  
Difference Equations ◽  
Higher Order ◽  
Linear Difference Equations ◽  
Order Linear

scholarly journals Study of the growth properties of meromorphic solutions of higher-order linear difference equations

2021 ◽  
Author(s):  
Benharrat Belaïdi ◽  
Rachid Bellaama
Keyword(s):  
Difference Equations ◽  
Meromorphic Functions ◽  
Higher Order ◽  
Complex Numbers ◽  
Meromorphic Solutions ◽  
Linear Difference Equations ◽  
Order Linear ◽  
Early Results ◽  
Growth Properties ◽  
Homogeneous Linear

AbstractIn this paper, we investigate the growth of meromorphic solutions of homogeneous and non-homogeneous linear difference equations $$\begin{aligned} A_{k}(z)f(z+c_{k})+\cdots +A_{1}(z)f(z+c_{1})+A_{0}(z)f(z)= & {} 0, \\ A_{k}(z)f(z+c_{k})+\cdots +A_{1}(z)f(z+c_{1})+A_{0}(z)f(z)= & {} F, \end{aligned}$$ A k ( z ) f ( z + c k ) + ⋯ + A 1 ( z ) f ( z + c 1 ) + A 0 ( z ) f ( z ) = 0 , A k ( z ) f ( z + c k ) + ⋯ + A 1 ( z ) f ( z + c 1 ) + A 0 ( z ) f ( z ) = F , where $$A_{k}\left( z\right) ,\ldots ,A_{0}\left( z\right) ,$$ A k z , … , A 0 z , $$F\left( z\right) $$ F z are meromorphic functions and $$c_{j}$$ c j $$\left( 1,\ldots ,k\right) $$ 1 , … , k are non-zero distinct complex numbers. Under some conditions on the coefficients, we extend early results due to Zhou and Zheng, Belaïdi and Benkarouba.

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