A Hochstadt-Lieberman theorem for integro-differential operator (Q2867739)
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scientific article; zbMATH DE number 6241508
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A Hochstadt-Lieberman theorem for integro-differential operator |
scientific article; zbMATH DE number 6241508 |
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20 December 2013
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half inverse problem
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Sturm-Liouville operator
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integro-differential operator
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A Hochstadt-Lieberman theorem for integro-differential operator (English)
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The authors consider a boundary value problem \(L=L(q,M)\) of the form NEWLINE\[NEWLINE -y''+q(x)y+\int_0^x M(x-t)y(t)\,dt=\lambda y, \quad x\in(0,\pi), \quad y(0)=y(\pi)=0, NEWLINE\]NEWLINE where \(q,\; M\) are real-valued functions and \(q\in L_2(0,\pi),\) \(M\in L(0,\pi).\) They study uniqueness of recovering the function \(q(x)\) on \((0,\pi/2)\) from the spectrum of \(L,\) provided that \(q\) on \((\pi/2,\pi)\) and \(M\) on \((0,\pi)\) are known a priori.
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