Hausdorff-Young inequality for the eigenfunctions and associated functions of a differential operator of second order

1987 ◽  
Vol 42 (3) ◽  
pp. 726-732 ◽  
Author(s):  
Kh. M. Karov
Keyword(s):  
Differential Operator ◽  
Young Inequality ◽  
Second Order ◽  
Associated Functions ◽  
Eigenfunctions And Associated Functions

scholarly journals Basis Properties of Eigenfunctions of Second-Order Differential Operators with Involution

2012 ◽  
Vol 2012 ◽  
pp. 1-6 ◽  
Author(s):  
Asylzat Kopzhassarova ◽  
Abdizhakhan Sarsenbi
Keyword(s):  
Differential Operator ◽  
Differential Operators ◽  
Second Order ◽  
Ordinary Differential Operator ◽  
Spectral Problems ◽  
Associated Functions ◽  
Eigenfunctions And Associated Functions

We study the basis properties of systems of eigenfunctions and associated functions for one kind of generalized spectral problems for a second-order ordinary differential operator.

scholarly journals Nonlocal boundary value problem for second order abstract elliptic differential equation

1999 ◽  
Vol 4 (3) ◽  
pp. 153-168 ◽  
Author(s):  
Mohamed Denche
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
Second Order ◽  
Cylindrical Domain ◽  
Nonlocal Boundary Value Problem ◽  
Abstract Differential Equations ◽  
Associated Functions ◽  
Eigenfunctions And Associated Functions ◽  
Coercive Solvability

We establish conditions that guarantee Fredholm solvability in the Banach spaceLpof nonlocal boundary value problems for elliptic abstract differential equations of the second order in an interval. Moreover, in the spaceL2we prove in addition the coercive solvability, and the completeness of root functions (eigenfunctions and associated functions). The obtained results are then applied to the study of a nonlocal boundary value problem for Laplace equation in a cylindrical domain.

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