Method of Spectral Mappings in the Inverse Problem Theory

By Vjacheslav A. Yurko. 2002

272 citations recorded by the source corpus.

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In Mathematical Physics

Citations in the corpus

Inverse spectral problems for differential operators on arbitrary compact graphs (2010, result): “We also note that the results and the methods of the theory of inverse spectral problems can be useful for investigating inverse problems for partial differential equations (see [15]).”
Spectral problems for Sturm–Liouville operator with boundary and jump conditions linearly dependent on the eigenparameter (2012, methodology): “The inverse problem for discontinuous Sturm–Liouville operator with Dirichlet conditions was given in [17] and [20].”
A uniqueness theorem for the boundary value problems with non-linear dependence on the spectral parameter in the boundary conditions (2009, background): “The functions ’(x, n) and (x, n) are corresponding eigenfunctions, and ðx, nÞ 1⁄4 n’ðx, nÞ, n 61⁄4 0: Clearly, the proof this Lemma completely repeats the similar Lemma which can be found in [4,15].”
On half inverse problem for differential pencils with the spectral parameter in boundary conditions (2011, background): “Such problems play an important role inmathematics and havemany applications in natural sciences and engineering (see [7]–[12] and the references therein).”
Incomplete Inverse Spectral and Nodal Problems for Differential Pencils (2011, background): “Such problems play an important role in mathematics and have many applications in natural sciences and engineering (see [6–11, and the references therein]).”
On inverse spectral problem for non-selfadjoint Sturm–Liouville operator on a finite interval (2007, methodology): “Using the main equation (35) and the method of spectral mappings [10,11] one can also obtain necessary and sufficient conditions for the solvability of the inverse problem similarly to the case of a simple spectrum [7].”
On an Inverse Spectral Problem for a Convolution Integro-differential Operator (2007, background): “The greatest success in the inverse problem theory has been achieved for the Sturm–Liouville operator (see the historical reviews in [3–5]) and afterwards for differential operators of an arbitrary order (see [1, 7, 8]).”
Definitions and examples of inverse and ill-posed problems (2008, background): “In some cases, the eigenvalues of the corresponding differential operator ∆U − ∇ ln ρ · ∇U = λU and various eigenfunction characteristics are known (inverse spectral problems) (Levitan , 1987; Yurko, 2002).”