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On the equiconvergence of eigenfunction expansions for a first-order functional-differential operator on a cycle-containing graph with two edges. (English. Russian original) Zbl 1152.34044

Differ. Equ. 43, No. 12, 1638-1647 (2007); translation from Differ. Uravn. 43, No. 12, 1597-1605 (2007).
From the paper: Let the operator \(L\) be defined by
\[ \begin{aligned} Ly&= \binom {\alpha_1y_1'(x)+ \alpha_2y_1'(1-x)+ p_{11}(x)y_1(x)+ p_{12}(x) y_1(1-x)} {\beta_1y_2'(x)+ \beta_2y_2'(1-x)+ p_{21}(x)y_2(x)+ p_{22}(x) y_2(1-x)},\\ y(x)&= (y_1(x),y_2(x))^T, \quad x\in [0,1],\\ y_1(0)&=y_1(1)= y_2(0), \end{aligned} \] where \(\alpha_1^2\neq \alpha_2^2\), \(\beta_1^2\neq \beta_2^2\), and \(p_{ij}(x)\in C^1[0,1]\).
The main result of the present paper is stated as an equiconvergence theorem for the Fourier series of an arbitrary function \(f(x)\) in root functions of the operator \(L\) and the trigonometric series of the function \(f(x)\).

MSC:

34K10 Boundary value problems for functional-differential equations
Full Text: DOI

References:

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