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A qualitative approach to inverse scattering theory / Fioralba Cakoni, David Colton.

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Author/Creator:
Cakoni, Fioralba, author.
Language:
English.
Publication date:
2014
Publication:
New York : Springer, [2014]
Format:
  • Book
  • x, 297 pages : illustrations ; 25 cm.
Note:
Previously published as: Qualitative methods in inverse scattering theory.
Bibliography:
Includes bibliographical references (pages 287-294) and index.
Contents:
  • Functional analysis and Sobolev spaces
  • Normed spaces
  • Bounded linear operators
  • Adjoint operator
  • Sobolev space Hp (...)
  • Sobolev space Hp (dD)
  • Ill-posed problems
  • Regularization methods
  • Singular value decomposition
  • Tikhonov regularization
  • Scattering by imperfect conductors
  • Maxwell's equations
  • Bessel functions
  • Direct scattering problem
  • Inverse scattering problems for imperfect conductors
  • Far-field patterns
  • Uniqueness theorems for inverse problem
  • Linear sampling method
  • Determination of surface impedance
  • Limited aperture data
  • Near-field data
  • Scattering by orthotropic media
  • Maxwell equations for an orthotropic medium
  • Mathematical formulation of direct scattering problem
  • Variational methods
  • Solution of direct scattering problem
  • Inverse scattering problems for orthotropic media
  • Formulation of inverse problem
  • Interior transmission problem
  • Transmission eigenvahle problern
  • The case n = 1
  • The case n ... 1
  • Discreteness of transmission eigenvalues
  • Existence of transmission eigenvalues for n ... 1
  • Uniqueness
  • Linear sampling method
  • Determination of transmission eigenvalues from far-field data
  • Factorization methods
  • Factorization method for obstacle scattering
  • Preliminary results
  • Properties of far-field operator
  • Factorization method
  • Factorization method for an inhomogeneous medium
  • Preliminary results
  • Properties of far-field operator
  • Factorization method
  • Justification of linear sampling method
  • Closing remarks
  • Mixed boundary value problems
  • Scattering by a partially coated perfect conductor
  • Inverse scattering problem for partially coated perfect conductor
  • Numerical examples
  • Scattering by partially coated dielectric
  • Inverse scattering problem for partially coated dielectric
  • Numerical examples
  • Scattering by cracks
  • Inverse scattering problem for cracks
  • Numerical examples
  • Inverse spectral problems for transmission eigenvalues
  • Entire functions
  • Transformation operators
  • Transmission eigenvalues
  • An inverse spectral theorem
  • A glimpse at maxwell's equations
  • References
  • Index.
Contributor:
Colton, David L., 1943- author.
Included Work:
Cakoni, Fioralba. Qualitative methods in inverse scattering theory, author.
Available in another form:
9781461488279 (online)
(GyWOH)har130547821
Series:
Applied mathematical sciences, 0066-5452 ; Volume 188
Applied mathematical sciences (Springer-Verlag New York Inc.) ; v. 188.
Subjects:
ISBN:
9781461488262
1461488265

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