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arXiv · 1703.01708

Inverse resonance problems for the Schroedinger operator on the real line with mixed given data

Xiao-Chuan Xu·Chuan-Fu Yang
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Abstract

In this work, we study inverse resonance problems for the Schrödinger operator on the real line with the potential supported in $[0,1]$. In general, all eigenvalues and resonances can not uniquely determine the potential. (i) It is shown that if the potential is known a priori on $[0,1/2]$, then the unique recovery of the potential on the whole interval from all eigenvalues and resonances is valid. (ii) If the potential is known a priori on $[0,a]$, then for the case $a>1/2$, infinitely many eigenvalues and resonances can be missing for the unique determination of the potential, and for the case $a<1/2$, all eigenvalues and resonances plus a part of so-called sign-set can uniquely determine the potential. (iii) It is also shown that all eigenvalues and resonances, together with a set of logarithmic derivative values of eigenfunctions and wave-functions at $1/2$, can uniquely determine the potential.

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Xiao-Chuan Xu, Chuan-Fu Yang. 2017-09-13. Inverse resonance problems for the Schroedinger operator on the real line with mixed given data. https://doi.org/10.1007/s11005-017-1003-6

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