Results 251 to 260 of about 342,447 (287)

On an inverse spectral problem

Russian Journal of Mathematical Physics, 2017
The author considers the inverse spectral problem of reconstructing a function \(Q\) appearing in \[ (Qy')' +\lambda (y(x)-ky''(x))=0\text{ for }0\leq x \leq 1, \] where \(y\) is subject to \[ y(0)=y(1)=0,\, \int_0^1 y(x)dx=0 \] for \(k>0\). The sought \(Q\) is normalized by \(\int_0^1 Q(x)dx=1\) and the question is to find \(Q\) that minimizes the ...
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Inverse spectral problem for quantum graphs

Journal of Physics A: Mathematical and General, 2005
Summary: The inverse spectral problem for the Laplace operator on a finite metric graph is investigated. It is shown that this problem has a unique solution for graphs with rationally independent edges and without vertices having valence 2. To prove the result, a trace formula connecting the spectrum of the Laplace operator with the set of periodic ...
Kurasov, Pavel, Nowaczyk, Marlena
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New inverse spectral problem and its application

1997
The origin of inverse spectral problems lies in natural science, but the problems themselves are purely mathematical. At the beginning these problems attracted attention of mathematicians by their nonstandard physical contents. But we think that today their place in mathematical physics is determined rather by the unexpected connection between inverse ...
Anne Boutet de Monvel, Vladimir Marchenko   +1 more
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Windowed Spectral Regularization of Inverse Problems

SIAM Journal on Scientific Computing, 2011
Regularization is used in order to obtain a reasonable estimate of the solution to an ill-posed inverse problem. One common form of regularization is to use a filter to reduce the influence of components corresponding to small singular values, perhaps using a Tikhonov least squares formulation.
Julianne Chung, Glenn Easley, Dianne P. O'Leary   +2 more
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Lq -inverse spectral problems for semilinear Sturm–Liouville problems

Nonlinear Analysis: Theory, Methods & Applications, 2008
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Inverse Spectral Problems for Transmission Eigenvalues

2013
We previously encountered transmission eigenvalues and their role in inverse scattering theory in Chap. 6. We now return to this topic and consider the inverse spectral problem for transmission eigenvalues in the simplest possible case, i.e., when the inhomogeneous medium is an isotropic spherically stratified medium in ℝ3 and the eigenfunctions ...
Fioralba Cakoni, David Colton
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Spectral Analysis of an Inverse Problem

2013
In this chapter we treat the solution of systems of linear equations in finite dimension spaces. This can be seen as examples of inverse reconstruction problems of Type I.We present a mathematical analysis of these linear inverse problems of finite dimension based on the spectral theorem.We study several aspects and behaviour of well-established ...
Francisco Duarte Moura Neto, Antônio José da Silva Neto   +1 more
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Riemann Hypothesis and Inverse Spectral Problems

2012
In this chapter, we provide an alternative formulation of the Riemann hypothesis in terms of a natural inverse spectral problem for fractal strings. After stating this inverse problem in Section 9.1, we show in Section 9.2 that its solution is equivalent to the nonexistence of critical zeros of the Riemann zeta function on a given vertical line.
Michel L. Lapidus, Machiel van Frankenhuijsen   +1 more
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Inverse spectral problem for delta potentials

JETP Letters, 2015
The scattering problem for the linear Schrodinger equation on the entire axis has been considered. Conditions under which the knowledge of the discrete spectrum of the Schrodinger operator is sufficient for the reconstruction of the potential have been determined.
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Inverse Spectral Problems for Differential Systems

2019
Inverse problems of spectral analysis for non-selfadjoint systems of ordinary differential equations are studied. We establish properties of the spectral characteristics, give statements of the inverse problems, prove uniqueness theorems, obtain algorithms for the solutions of the inverse problems and provide necessary and sufficient conditions for ...
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