scholarly journals On Multiple Completeness of the Root Functions of a Certain Class of Pencils of Differential Operators with Constant Coefficients

2014 ◽  
Vol 14 (4) ◽  
pp. 574-584 ◽  
Author(s):  
V. S. Rykhlov ◽  
◽  
O. V. Blinkova ◽  
Keyword(s):  
Differential Operators ◽  
Root Functions ◽  
Multiple Completeness ◽  
Constant Coefficients

scholarly journals On Multiple Completeness of the Root Functions of Ordinary Differential Polynomial Pencil with Constant Coefficients

2017 ◽  
Vol 63 (2) ◽  
pp. 340-361
Author(s):  
V S Rykhlov
Keyword(s):  
Differential Operators ◽  
Sufficient Conditions ◽  
Differential Polynomial ◽  
Finite Segment ◽  
Root Functions ◽  
Multiple Completeness ◽  
Integrable Functions ◽  
Constant Coefficients ◽  
System Of Root Functions ◽  
Square Integrable Functions

In the space of square integrable functions on a finite segment we consider a class of polynomial pencils of nth-order ordinary differential operators with constant coefficients and two-point boundary-value conditions (at the edges of the segment). We suppose that roots of the characteristic equation of pencils of this class are simple and nonzero. We establish sufficient conditions for m-multiple completeness (1≤m≤n) of the system of root functions of pencils from this class in the space of square integrable functions on this segment.

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