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...

Full description

Saved in:
Bibliographic Details
Published inActa Mathematicae Applicatae Sinica Vol. 37; no. 2; pp. 287 - 298
Main Authors Yang, Chuan-fu, Wang, Feng, Huang, Zhen-you
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.04.2021
Springer Nature B.V
EditionEnglish series
Subjects
Applications of Mathematics
Boundary conditions
Eigenvalues
Existence theorems
Math Applications in Computer Science
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Operators
Theoretical
Ambarzumyan’s theorem
inverse spectral problem
65L09
Dirac operator
vectorial Sturm-Liouville operator
34L05
Online AccessGet full text

Cover

More Information
Summary: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.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:0168-9673
1618-3932
DOI:10.1007/s10255-021-1007-y