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Inverse problems for radial Schrodinger operators with the missing part of eigenvalues

Science China Mathematics 2023年第8期66卷 1831-1848页

作者： Xin-Jian Xu Chuan-Fu Yang vjacheslav a.yurko Ran Zhang Department of Mathematics School of Mathematics and StatisticsNanjing University of Science and TechnologyNanjing 210094China Department of Mathematics Saratov State UniversitySaratov 410012Russia Department of Mathematics School of ScienceNanjing University of Posts and TelecommunicationsNanjing 210023Chin

We study inverse spectral problems for radial Schrodinger operators in L^(2)(0,1).It is well known that for a radial Schrodinger operator,two spectra for the different boundary conditions can uniquely determine the ***,if the spectra corresponding to the radial Schrodinger operators with the two potential functions miss a finite number of eigenvalues,what is the relationship between the two potential functions?Inspired by Hochstadt(1973)'s work,which handled the Sturm-Liouville operator with the potential q∈L^(1)(0,1),we give a corresponding result for radial Schrodinger operators with a larger class of potentials than L^(1)(0,1).When q∈L^(1)(0,1),we also consider the case where the spectra corresponding to the radial Schrodinger operators with the two potential functions miss an infinite number of eigenvalues and the eigenvalues are close in some sense.

关键词： radial Schrodinger operator Bessel operator inverse spectral problem

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Inverse problems for radial Schr?dinger operators with the missing part of eigenvalues

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Science China Mathematics 2023年第8期 1831-1848页

作者： Xin-Jian Xu Chuan-Fu Yang vjacheslav a.yurko Ran Zhang Department of Mathematics School of Mathematics and StatisticsNanjing University of Science and Technology Department of Mathematics Saratov State University Department of Mathematics School of ScienceNanjing University of Posts and Telecommunications

We study inverse spectral problems for radial Schr?dinger operators in L2（0, 1）. It is well known that for a radial Schr?dinger operator, two spectra for the different boundary conditions can uniquely determine the potential. However, if the spectra corresponding to the radial Schr?dinger operators with the two potential functions miss a finite number of eigenvalues, what is the relationship between the two potential functions?Inspired by Hochstadt（1973）'s work, which handled the Sturm-Liouville operator with the potential q ∈ L1（0, 1）,we give a corresponding result for radial Schr?dinger operators with a larger class of potentials than L1（0, 1）.When q ∈ L1（0, 1）, we also consider the case where the spectra corresponding to the radial Schr?dinger operators with the two potential functions miss an infinite number of eigenvalues and the eigenvalues are close in some sense.

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