Ambarzumyan Theorems for Dirac Operators
We consider the inverse eigenvalue problems for stationary Dirac systems with differentiable self-adjoint matrix potential. The theorem of Ambarzumyan for a Sturm-Liouville problem is extended to Dirac operators, which are subject to separation boundary conditions or periodic (semi-periodic) boundar...
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| Published in | Acta Mathematicae Applicatae Sinica Vol. 37; no. 2; pp. 287 - 298 |
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| Format | Journal Article |
| Language | English |
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Berlin/Heidelberg
Springer Berlin Heidelberg
01.04.2021
Springer Nature B.V |
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| ISSN | 0168-9673 1618-3932 |
| DOI | 10.1007/s10255-021-1007-y |
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| Abstract | We consider the inverse eigenvalue problems for stationary Dirac systems with differentiable self-adjoint matrix potential. The theorem of Ambarzumyan for a Sturm-Liouville problem is extended to Dirac operators, which are subject to separation boundary conditions or periodic (semi-periodic) boundary conditions, and some analogs of Ambarzumyan’s theorem are obtained. The proof is based on the existence and extremal properties of the smallest eigenvalue of corresponding vectorial Sturm-Liouville operators, which are the second power of Dirac operators. |
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| AbstractList | We consider the inverse eigenvalue problems for stationary Dirac systems with differentiable self-adjoint matrix potential. The theorem of Ambarzumyan for a Sturm-Liouville problem is extended to Dirac operators, which are subject to separation boundary conditions or periodic (semi-periodic) boundary conditions, and some analogs of Ambarzumyan’s theorem are obtained. The proof is based on the existence and extremal properties of the smallest eigenvalue of corresponding vectorial Sturm-Liouville operators, which are the second power of Dirac operators. |
| Author | Huang, Zhen-you Yang, Chuan-fu Wang, Feng |
| Author_xml | – sequence: 1 givenname: Chuan-fu surname: Yang fullname: Yang, Chuan-fu email: tchuanfuyang@njust.edu.cn organization: Department of Applied Mathematics, Nanjing University of Science and Technology – sequence: 2 givenname: Feng surname: Wang fullname: Wang, Feng organization: Department of Applied Mathematics, Nanjing University of Science and Technology – sequence: 3 givenname: Zhen-you surname: Huang fullname: Huang, Zhen-you organization: Department of Applied Mathematics, Nanjing University of Science and Technology |
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| Keywords | Ambarzumyan’s theorem inverse spectral problem 65L09 Dirac operator vectorial Sturm-Liouville operator 34L05 |
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| SubjectTerms | Applications of Mathematics Boundary conditions Eigenvalues Existence theorems Math Applications in Computer Science Mathematical and Computational Physics Mathematics Mathematics and Statistics Operators Theoretical |
| Title | Ambarzumyan Theorems for Dirac Operators |
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