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On a theorem of Ambarzumian

Published online by Cambridge University Press:  12 July 2007

Miklós Horváth
Miklós Horváth
Affiliation:
Department of Analysis, Institute of Mathematics, Technical University of Budapest, H1111 Budapest, Műegyetem rkp. 3-9, Hungary (horvath@math.bme.hu)
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Abstract

We consider the eigenvalue problem for the one-dimensional (stationary) Dirac operator with some boundary conditions. We prove that if the spectrum is the same as the spectrum belonging to the zero potential, then the potential is actually zero. The analogous statement for the Schrödinger operator is due to Ambarzumian. The proof is based on the fact that the (generalized) moments of a function cannot have alternating signs unless the moments are zero (see §2).

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 131 , Issue 4 , August 2001 , pp. 899 - 907
Copyright
Copyright © Royal Society of Edinburgh 2001

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