On properties of systems of root functions of well-posed boundary value problems for the second order differential operator (Q2910445)
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scientific article; zbMATH DE number 6080740
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On properties of systems of root functions of well-posed boundary value problems for the second order differential operator |
scientific article; zbMATH DE number 6080740 |
Statements
11 September 2012
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bi-orthogonal systems
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system of root functions
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well-posed boundary value problems
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nonlocal boundary conditions
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resolvent
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On properties of systems of root functions of well-posed boundary value problems for the second order differential operator (English)
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The explicit system of root functions for the second differential operator defining a non-local boundary value problem of the form NEWLINE\[NEWLINE\begin{aligned} & -y''(x)=f(x),\quad 0<x<1, \\ & y(0)- \int_{0}^{1}(-y''(x))\overline{\sigma(x)}dx=0,\\ & y'(0)=0,\end{aligned}NEWLINE\]NEWLINE with \(\sigma(x)\in L_{2}(0,1)\) is obtained.NEWLINENEWLINEA new method of constructing and investigating the bi-orthogonality of the system of root functions is proposed.
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