منابع مشابه
On Local Borg–Marchenko Uniqueness Results
We provide a new short proof of the following fact, first proved by one of us in 1998: If two Weyl–Titchmarsh m-functions, mj(z), of two Schrödinger operators Hj = − d2 dx2 + qj , j = 1, 2 in L2((0, R)), 0 < R ≤ ∞, are exponentially close, that is, |m1(z) − m2(z)| = |z|→∞ O(e −2 Im(z)a), 0 < a < R, then q1 = q2 a.e. on [0, a]. The result applies to any boundary conditions at x = 0 and x = R and...
متن کاملBorg–marchenko-type Uniqueness Results for Cmv Operators
We prove local and global versions of Borg–Marchenko-type uniqueness theorems for half-lattice and full-lattice CMV operators (CMV for Cantero, Moral, and Velázquez [15]). While our half-lattice results are formulated in terms of Weyl–Titchmarsh functions, our full-lattice results involve the diagonal and main off-diagonal Green’s functions.
متن کاملThe Borg-Marchenko Theorem with a Continuous Spectrum
The Schrödinger equation is considered on the half line with a selfadjoint boundary condition when the potential is real valued, integrable, and has a finite first moment. It is proved that the potential and the two boundary conditions are uniquely determined by a set of spectral data containing the discrete eigenvalues for a boundary condition at the origin, the continuous part of the spectral...
متن کاملWeyl–titchmarsh M-function Asymptotics, Local Uniqueness Results, Trace Formulas, and Borg-type Theorems for Dirac Operators
We explicitly determine the high-energy asymptotics for Weyl– Titchmarsh matrices associated with general Dirac-type operators on half-lines and on R. We also prove new local uniqueness results for Dirac-type operators in terms of exponentially small differences of Weyl–Titchmarsh matrices. As concrete applications of the asymptotic high-energy expansion we derive a trace formula for Dirac oper...
متن کاملar X iv : m at h / 99 10 08 9 v 1 [ m at h . SP ] 1 8 O ct 1 99 9 ON LOCAL BORG - MARCHENKO UNIQUENESS RESULTS
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 H j = − d 2 dx 2 + q j , j = 1, 2 in L 2 ((0, R)), 0 < R ≤ ∞, are exponentially close, that is, |m 1 (z) − m 2 (z)| = |z|→∞ O(e −2 Im(z 1/2)a), 0 < a < R, then q 1 = q 2 a.e. on [0, a]. The result applies to any boundary conditions at x...
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ژورنال
عنوان ژورنال: Communications in Mathematical Physics
سال: 2000
ISSN: 0010-3616,1432-0916
DOI: 10.1007/s002200050812