Operators and applications

Väth, Martin

doi:10.1007/bfb0093553

Cited by 3 publications

References 18 publications

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A New Approach to Inverse Spectral Theory, I. Fundamental Formalism

Simon¹

1999

The Annals of Mathematics

147

231

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We present a new approach (distinct from Gel ′ fand-Levitan) to the theorem of Borg-Marchenko that the m-function (equivalently, spectral measure) for a finite interval or half-line Schrödinger operator determines the potential. Our approach is an analog of the continued fraction approach for the moment problem. We prove there is a representation for the m-functionis a function of q on [0, a] and vice-versa. A key role is played by a differential equation that A obeys after allowing x-dependence:Among our new results are necessary and sufficient conditions on the mfunctions for potentials q 1 and q 2 for q 1 to equal q 2 on [0, a].

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A New Approach to Inverse Spectral Theory, I. Fundamental Formalism

Simon¹

1999

The Annals of Mathematics

147

231

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On the Inverse Problem for Sturm-Liouville Operator With a Nonlinear Spectral Parameter in the Boundary Condition

Mamedov¹

2009

Journal of the Korean Mathematical Society

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Abstract. The inverse scattering problem is investigated for some second order differential equation with a nonlinear spectral parameter in the boundary condition on the half line [0, ∞). In the present paper the coefficient of spectral parameter is not a pure imaginary number and the boundary value problem is not selfadjoint. We define the scattering data of the problem, derive the main integral equation and show that the potential is uniquely recovered.

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Fixed points and completeness in metric and in generalized metric spaces

Cobzaş

2015

Preprint

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The famous Banach Contraction Principle holds in complete metric spaces, but completeness is not a necessary condition -there are incomplete metric spaces on which every contraction has a fixed point. The aim of this paper is to present various circumstances in which fixed point results imply completeness. For metric spaces this is the case of Ekeland variational principle and of its equivalent -Caristi fixed point theorem. Other fixed point results having this property will be also presented in metric spaces, in quasi-metric spaces and in partial metric spaces. A discussion on topology and order and on fixed points in ordered structures and their completeness properties is included as well.

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Operators and applications

Cited by 3 publications

References 18 publications

A New Approach to Inverse Spectral Theory, I. Fundamental Formalism

A New Approach to Inverse Spectral Theory, I. Fundamental Formalism

On the Inverse Problem for Sturm-Liouville Operator With a Nonlinear Spectral Parameter in the Boundary Condition

Fixed points and completeness in metric and in generalized metric spaces

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