Linear ordinary differential equations with constant coefficients over a Banach algebra

2008 ◽  
Vol 84 (3-4) ◽  
pp. 342-355
Author(s):  
V. P. Derevenskii
Keyword(s):  
Differential Equations ◽  
Banach Algebra ◽  
Ordinary Differential Equations ◽  
Linear Ordinary Differential Equations ◽  
Constant Coefficients

From linear recurrence relations to linear ODEs with constant coefficients

2016 ◽  
Vol 15 (06) ◽  
pp. 1650109 ◽  
Author(s):  
L. Gatto ◽  
D. Laksov
Keyword(s):  
Differential Equations ◽  
Laplace Transform ◽  
Ordinary Differential Equations ◽  
Recurrence Relations ◽  
Schubert Calculus ◽  
Linear Recurrence ◽  
Linear Ordinary Differential Equations ◽  
Constant Coefficients ◽  
Linear Odes

Linear Ordinary Differential Equations (ODEs) with constant coefficients are studied by looking in general at linear recurrence relations in a module with coefficients in an arbitrary [Formula: see text]-algebra. The bridge relating the two theories is the notion of formal Laplace transform associated to a sequence of invertibles. From this more economical perspective, generalized Wronskians associated to solutions of linear ODEs will be revisited, mentioning their relationships with Schubert Calculus for Grassmannians.

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