The Inverse Problem of Electromagnetic Scattering Theory. I. A Uniqueness Theorem for Cylinders

1966 ◽  
Vol 45 (1-4) ◽  
pp. 179-187 ◽  
Author(s):  
R. Mireles
Keyword(s):  
Inverse Problem ◽  
Uniqueness Theorem ◽  
Electromagnetic Scattering ◽  
Scattering Theory

On the inverse problem in quantum scattering theory

2009 ◽  
Vol 28 (S19) ◽  
pp. 457-466
Author(s):  
Erkki Brändas ◽  
Erik Engdahl ◽  
Magnus Rittby ◽  
Nils Elander
Keyword(s):  
Inverse Problem ◽  
Scattering Theory ◽  
Quantum Scattering ◽  
Quantum Scattering Theory

A uniqueness theorem in scattering theory

1984 ◽  
Vol 102 (5-6) ◽  
pp. 218-219 ◽  
Author(s):  
A.G. Ramm
Keyword(s):  
Uniqueness Theorem ◽  
Scattering Theory

scholarly journals Recovering singular differential operators on noncompact star-type graphs from Weyl functions

2011 ◽  
Vol 42 (2) ◽  
pp. 223-236
Author(s):  
V. Yurko
Keyword(s):  
Inverse Problem ◽  
Uniqueness Theorem ◽  
Differential Operators ◽  
Spectral Characteristics ◽  
Method Of Spectral Mappings ◽  
Weyl Functions

Bessel-type differential operators on noncompact star-type graphs are studied. We establish properties of the spectral characteristics and then we investigate the inverse problem of recovering the operator from the so-called Weyl vector. For this inverse problem we prove a uniqueness theorem and propose a procedure for constructing the solution using the method of spectral mappings.

Inverse problem for one-dimensional wave equation with matrix potential

2019 ◽  
Vol 27 (2) ◽  
pp. 217-223 ◽  
Author(s):  
Ammar Khanfer ◽  
Alexander Bukhgeim
Keyword(s):  
Inverse Problem ◽  
Wave Equation ◽  
Uniqueness Theorem ◽  
Cauchy Data ◽  
Global Uniqueness ◽  
One Dimensional ◽  
Matrix Potential ◽  
The Matrix ◽  
Real Matrices ◽  
Dimensional Wave

AbstractWe prove a global uniqueness theorem of reconstruction of a matrix-potential {a(x,t)} of one-dimensional wave equation {\square u+au=0}, {x>0,t>0}, {\square=\partial_{t}^{2}-\partial_{x}^{2}} with zero Cauchy data for {t=0} and given Cauchy data for {x=0}, {u(0,t)=0}, {u_{x}(0,t)=g(t)}. Here {u,a,f}, and g are {n\times n} smooth real matrices, {\det(f(0))\neq 0}, and the matrix {\partial_{t}a} is known.

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