Abel summability of a system of root functions for a nonlocal problem with integral conditions

1999 ◽  
Vol 65 (5) ◽  
pp. 672-675 ◽  
Author(s):  
V. V. Pod″yapol’skii
Keyword(s):  
Nonlocal Problem ◽  
Integral Conditions ◽  
Abel Summability ◽  
Root Functions ◽  
System Of Root Functions

scholarly journals ON CERTAIN NONLOCAL PROBLEM FOR HYPERBOLIC EQUATION WITH INTEGRAL CONDITIONS OF THE FIRST KIND

2017 ◽  
Vol 17 (5) ◽  
pp. 29-36
Author(s):  
A.V. Duzheva
Keyword(s):  
Hyperbolic Equation ◽  
Existence And Uniqueness ◽  
Nonlocal Problem ◽  
Integral Condition ◽  
Generalized Solution ◽  
Integral Conditions

In this article, we consider a nonlocal problem for hyperbolic equation with integral conditions of the first kind. The main goal of this article is to show the method which allows to reduce posed problem to the problem with integral condition of the second kind. Existence and uniqueness of generalized solution is proved.

scholarly journals Riesz Inequality for the System of Root Functions of Second Order Ordinary Differential Operator

2020 ◽  
Vol 19 ◽  
Keyword(s):  
Differential Operator ◽  
Sufficient Conditions ◽  
Second Order ◽  
Ordinary Differential Operator ◽  
Root Functions ◽  
Riesz Property ◽  
System Of Root Functions ◽  
The Given ◽  
Riesz Inequality

An ordinary differential operator of second order with coefficients is considered. The Riesz property of the system of root functions of the given operator is studied. The criterion of Bessel property in 2 L , of root functions system is established and use it to obtain sufficient conditions for the Riesz property of a system of normalized root functions of this operator in p L .

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