The invertibility of elliptic operators with constant coefficients acting on generalized measures in an infinite-dimensional space

1977 ◽  
Vol 16 (3) ◽  
pp. 326-331
Author(s):  
V. Yu. Bentkus
Keyword(s):  
Dimensional Space ◽  
Elliptic Operators ◽  
Infinite Dimensional Space ◽  
Infinite Dimensional ◽  
Constant Coefficients

scholarly journals General Explicit Solution of Planar Weakly Delayed Linear Discrete Systems and Pasting Its Solutions

2014 ◽  
Vol 2014 ◽  
pp. 1-37 ◽  
Author(s):  
Josef Diblík ◽  
Hana Halfarová
Keyword(s):  
Dimensional Space ◽  
Discrete Systems ◽  
Infinite Dimensional Space ◽  
Initial Interval ◽  
Infinite Dimensional ◽  
Finite Dimensional ◽  
Linear Differential Systems ◽  
Constant Coefficients ◽  
Linear Differential ◽  
Linear Discrete Systems

Planar linear discrete systems with constant coefficients and delaysx(k+1)=Ax(k)+∑l=1n‍Blxl(k-ml)are considered wherek∈ℤ0∞:={0,1,…,∞},m1,m2,…,mnare constant integer delays,0<m1<m2<⋯<mn,A,B1,…,Bnare constant2×2matrices, andx:ℤ-mn∞→ℝ2. It is assumed that the considered system is weakly delayed. The characteristic equations of such systems are identical with those for the same systems but without delayed terms. In this case, after several steps, the space of solutions with a given starting dimension2(mn+1)is pasted into a space with a dimension less than the starting one. In a sense, this situation is analogous to one known in the theory of linear differential systems with constant coefficients and special delays when the initially infinite dimensional space of solutions on the initial interval turns (after several steps) into a finite dimensional set of solutions. For every possible case, explicit general solutions are constructed and, finally, results on the dimensionality of the space of solutions are obtained.

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