منابع مشابه
Inverse Resonance Scattering on the Half Line
For the Schrr odinger operator on the half line we prove the following results: the mapping from real compactly supported potentials to the associated Jost functions (in some class of entire functions) is one-to-one and onto. Moreover, we prove that such potential is uniquely determined by its bound states and resonances.
متن کاملInverse Scattering with Fixed Energy and an Inverse Eigenvalue Problem on the Half-line
Recently A. G. Ramm (1999) has shown that a subset of phase shifts δl, l = 0, 1, . . ., determines the potential if the indices of the known shifts satisfy the Müntz condition ∑ l =0,l∈L 1 l = ∞. We prove the necessity of this condition in some classes of potentials. The problem is reduced to an inverse eigenvalue problem for the half-line Schrödinger operators.
متن کاملInverse Scattering on the Line with Incomplete Scattering Data
The Schrödinger equation is considered on the line when the potential is real valued, compactly supported, and square integrable. The nonuniqueness is analyzed in the recovery of such a potential from the data consisting of the ratio of a corresponding reflection coefficient to the transmission coefficient. It is shown that there are a discrete number of potentials corresponding to the data and...
متن کاملInverse Spectral and Scattering Theory for the Half-Line Left-Definite Sturm-Liouville Problem
together with appropriate boundary conditions, in the space Lw of functions square integrable with respect to the weight w, i.e., the normsquare of the space is ‖u‖2 = ∫ |u|2w. A basic assumption for this to be possible is that w ≥ 0. In some situations of interest this is not the case, but instead one has p > 0, q ≥ 0. One may then use as a norm-square the integral ∫ (p|u′|2 + q|u|2), and a pr...
متن کاملBoundary Exchange Algebras and Scattering on the Half Line
Some algebraic aspects of field quantization in space-time with boundaries are discussed. We introduce an associative algebra BR, whose exchange properties are inferred from the scattering processes in integrable models with reflecting boundary conditions on the half line. The basic properties of BR are established and the Fock representations associated with certain involutions in BR are deriv...
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 1988
ISSN: 0022-247X
DOI: 10.1016/0022-247x(88)90422-2