Open Access Open Access  Restricted Access Subscription or Fee Access

On the Denseness of the Set of Scattering Amplitudes


(*) Corresponding author


Authors' affiliations


DOI's assignment:
the author of the article can submit here a request for assignment of a DOI number to this resource!
Cost of the service: euros 10,00 (for a DOI)

Abstract


It is proved that the set of scattering amplitudes {A(β,α,k)} with αєS2, known for all βєS2, where S2 is the unit sphere in R3, k>0 is fixed, k2 is not a Dirichlet eigenvalue of the Laplacian in D, is dense in L2(S2). Here A(β,α,k) is the scattering amplitude corresponding to an obstacle D, where D is a bounded domain with a boundary S. The boundary condition on S is the Dirichlet condition.
Copyright © 2017 Praise Worthy Prize - All rights reserved.

Keywords


Scattering Theory; Obstacle Scattering; Denseness of the Set of Scattering Amplitudes

Full Text:

PDF


References


B.Z. Katsenelenbaum, Problems of approximation of electromagnetic field, Nauka, Moscow, 1996. (in Russian)

A.G.Ramm, Scattering by obstacles, D.Reidel, Dordrecht, 1986.

A.G.Ramm, Inverse problems, Springer, New York, 2005.

A.G.Ramm, Solution to the Pompeiu problem and the related symmetry problem, Appl. Math. Lett., 63, (2017), 28-33.

A.G.Ramm, Completeness of the set of scattering amplitudes, Phys. Lett. A, 360, (2006), 22-25.

A.G.Ramm, Perturbation of zero surfaces, Global Journal of Math. Analysis, 5(1), (2017), 27-28.
Open access Journal: http://www.sciencepubco.com/index.php/GJMA/article/view/7474

A.G.Ramm, Completeness of the set {e^(ikβs) }, Global Journ. of Math. Analysis (GJMA), 5(2), (2017), 43-44.
Open access Journal: https://www.sciencepubco.com


Refbacks

  • There are currently no refbacks.


Please send any question about this web site to info@praiseworthyprize.com
Copyright © 2005-2024 Praise Worthy Prize