ISSN:
1432-0916
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
,
Physics
Notes:
Abstract: We provide a new short proof of the following fact, first proved by one of us in 1998: If two Weyl–Titchmarsh m-functions, m j (z), of two Schrödinger operators , j≡ 1,2 in L 2((0,R)), 0〈R≤∞, are exponentially close, that is, , 0〈a〈R, then q 1≡q 2 a.e. on [0,a]. The result applies to any boundary conditions at x≡ 0 and x≡R and should be considered a local version of the celebrated Borg–Marchenko uniqueness result (which is quickly recovered as a corollary to our proof). Moreover, we extend the local uniqueness result to matrix-valued Schrödinger operators.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/s002200050812
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