Conditions for the absolute and uniform convergence of the biorthogonal series corresponding to a differential operator

2008 ◽  
Vol 78 (2) ◽  
pp. 748-750 ◽  
Author(s):  
V. M. Kurbanov
Keyword(s):  
Differential Operator ◽  
Uniform Convergence ◽  
The Absolute ◽  
Biorthogonal Series

scholarly journals On Convergence of Orthogonal Expansion of a Function From the Class in the Eigenfunctions of a Differential Operator of the Third Order

2021 ◽  
Vol 18 ◽  
pp. 160-168
Author(s):  
Aygun Garayeva ◽  
Fatima Guliyeva
Keyword(s):  
Differential Operator ◽  
Uniform Convergence ◽  
Ordinary Differential Operator ◽  
Orthogonal Expansion ◽  
Third Order ◽  
The Third ◽  
The Absolute

We consider a third-order ordinary differential operator with summable coefficients. The absolute and uniform convergence of the orthogonal expansion of a function from the class in the eigenfunctionsof this operator is studied and the rate of uniform convergence of these expansions on is estimated

scholarly journals Absolute and Uniform Convergence of Spectral Expansion in the Eigenfunctions of a Third-Order Ordinary Differential Operator

2020 ◽  
Vol 19 ◽  
Keyword(s):  
Differential Operator ◽  
Uniform Convergence ◽  
Sufficient Conditions ◽  
Spectral Expansion ◽  
Ordinary Differential Operator ◽  
Third Order ◽  
Spectral Expansions

In this paper studied the convergence of spectral expansions of functions of the class W1 1 ( ) G ,G= ( ) 0,1 in eigenfunctions of an ordinary differential operator of third order with integral coefficients. Sufficient conditions for absolute and uniform convergence are obtained and the rate of uniform convergence of these expansions on the interval G is found.

scholarly journals A duality theorem for solutions of elliptic equations

1990 ◽  
Vol 13 (1) ◽  
pp. 73-85
Author(s):  
Pierre Blanchet
Keyword(s):  
Differential Operator ◽  
Uniform Convergence ◽  
Linear Space ◽  
Elliptic Equations ◽  
Duality Theorem ◽  
Adjoint Equation ◽  
Partial Differential Operator ◽  
Linear Partial Differential Operator ◽  
Elliptic Type ◽  
All Solutions

LetLbe a second order linear partial differential operator of elliptic type on a domainΩofℝmwith coefficients inC∞(Ω). We consider the linear space of all solutions of the equationLu=0onΩwith the topology of uniform convergence on compact subsets and describe the topological dual of this space. It turns out that this dual may be identified with the space of solutions of an adjoint equation “near the boundary” modulo the solutions of this adjoint equation on the entire domain.

scholarly journals Absolute and uniform convergence of spectral expansion of the function from the class W1p(g), p > 1, in eigenfunctions of third order differential operator

2017 ◽  
Vol 101 (115) ◽  
pp. 169-182
Author(s):  
V.M. Kurbanov ◽  
E.B. Akhundova
Keyword(s):  
Differential Operator ◽  
Convergence Rate ◽  
Uniform Convergence ◽  
Spectral Expansion ◽  
Ordinary Differential Operator ◽  
Order Differential Operator ◽  
Third Order ◽  
Uniform Convergence Rate

We study an ordinary differential operator of third order and absolute and uniform convergence of spectral expansion of the function from the class W1p(G), G = (0,1), p > 1, in eigenfunctions of the operator. Uniform convergence rate of this expansion is estimated.

The Absolute and Uniform Convergence of Infinite Improper Integrals

1988 ◽  
Vol 95 (2) ◽  
pp. 124-126
Author(s):  
David J. Hallenbeck ◽  
Katarzyna Tkaczyńska
Keyword(s):  
Uniform Convergence ◽  
Improper Integrals ◽  
The Absolute

The Absolute and Uniform Convergence of Infinite Improper Integrals

1988 ◽  
Vol 95 (2) ◽  
pp. 124
Author(s):  
David J. Hallenbeck ◽  
Katarzyna Tkaczynska
Keyword(s):  
Uniform Convergence ◽  
Improper Integrals ◽  
The Absolute
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