An operator integral in the multidimensional spectral inverse problem

1997 ◽  
Vol 85 (1) ◽  
pp. 1559-1577 ◽  
Author(s):  
M. I. Belishev ◽  
A. P. Kachalov
Keyword(s):  
Inverse Problem ◽  
Spectral Inverse Problem

scholarly journals An iterative method in a probabilistic approach to the spectral inverse problem

2010 ◽  
Vol 523 ◽  
pp. A44 ◽  
Author(s):  
F. F. Goryaev ◽  
S. Parenti ◽  
A. M. Urnov ◽  
S. N. Oparin ◽  
J.-F. Hochedez ◽  
...  
Keyword(s):  
Inverse Problem ◽  
Iterative Method ◽  
Probabilistic Approach ◽  
Spectral Inverse Problem

scholarly journals Joining Forces for Reconstruction Inverse Problems

Symmetry ◽  
2021 ◽  
Vol 13 (9) ◽  
pp. 1687
Author(s):  
Irene Sciriha
Keyword(s):  
Inverse Problem ◽  
Inverse Problems ◽  
Graph Matching ◽  
Isomorphism Problem ◽  
Reconstruction Problem ◽  
Graph Invariants ◽  
Minimal Set ◽  
Disconnected Graphs ◽  
Polynomial Reconstruction ◽  
Spectral Inverse Problem

A spectral inverse problem concerns the reconstruction of parameters of a parent graph from prescribed spectral data of subgraphs. Also referred to as the P–NP Isomorphism Problem, Reconstruction or Exact Graph Matching, the aim is to seek sets of parameters to determine a graph uniquely. Other related inverse problems, including the Polynomial Reconstruction Problem (PRP), involve the recovery of graph invariants. The PRP seeks to extract the spectrum of a graph from the deck of cards each showing the spectrum of a vertex-deleted subgraph. We show how various algebraic methods join forces to reconstruct a graph or its invariants from a minimal set of restricted eigenvalue-eigenvector information of the parent graph or its subgraphs. We show how functions of the entries of eigenvectors of the adjacency matrix A of a graph can be retrieved from the spectrum of eigenvalues of A. We establish that there are two subclasses of disconnected graphs with each card of the deck showing a common eigenvalue. These could occur as possible counter examples to the positive solution of the PRP.

SPECTRAL INVERSE PROBLEM IN SUPERSYMMETRIC QUANTUM MECHANICS

1993 ◽  
Vol 08 (23) ◽  
pp. 4123-4129 ◽  
Author(s):  
P.K. BERA ◽  
S. BHATTACHARYYA ◽  
B. TALUKDAR
Keyword(s):  
Inverse Problem ◽  
Quantum Mechanics ◽  
Hydrogen Atom ◽  
State Energy ◽  
Bound State ◽  
Quantization Condition ◽  
Energy Spectra ◽  
Conventional Theory ◽  
Bound State Energy ◽  
Spectral Inverse Problem

The supersymmetric WKB quantization condition is used to study the so-called spectral inverse problem. Wavefunctions for the harmonic oscillator and hydrogen atom are obtained from the knowledge of their bound-state energy spectra. The analysis presented is based essentially on a repackaging of the conventional theory of integral equations.

scholarly journals On a Spectral Inverse Problem in Perturbation Theory

2021 ◽  
Vol 17 (1) ◽  
pp. 95-115
Author(s):  
V.A. Marchenko ◽  
◽  
A.V. Marchenko ◽  
V.A. Zolotarev ◽  
◽  
...  
Keyword(s):  
Inverse Problem ◽  
Perturbation Theory ◽  
Spectral Inverse Problem

Spectral inverse problem for q-deformed harmonic oscillator

Pramana ◽  
2006 ◽  
Vol 67 (6) ◽  
pp. 1023-1035 ◽  
Author(s):  
P K Bera ◽  
J Datta
Keyword(s):  
Inverse Problem ◽  
Harmonic Oscillator ◽  
Spectral Inverse Problem

AN INVERSE PROBLEM IN THE DYNAMICAL REATOR THEORY

1982 ◽  
Vol 2 (1) ◽  
pp. 9-16 ◽  
Author(s):  
Dexing Feng ◽  
Guangtian Zhu
Keyword(s):  
Inverse Problem
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