Open Access
Issue
ESAIM: M2AN
Volume 54, Number 4, July-August 2020
Page(s) 1111 - 1138
DOI https://doi.org/10.1051/m2an/2019088
Published online 18 May 2020
  1. A.D. Agaltsov, T. Hohage and R.G. Novikov, Monochromatic identities for the Green function and uniqueness results for passive imaging. SIAM J. Appl. Math. 78 (2018) 2865–2890. [Google Scholar]
  2. A.D. Agaltsov, T. Hohage and R.G. Novikov, Global uniqueness in a passive inverse problem of helioseismology. Preprint arXiv:1907.05939 (2019). [Google Scholar]
  3. A. Alastuey, V. Ballenegger, F. Cornu and P.A. Martin, Exact results for thermodynamics of the hydrogen plasma: low-temperature expansions beyond Saha theory. J. Stat. Phys. 130 (2008) 1119–1176. [Google Scholar]
  4. G.S. Alberti and M. Santacesaria, Calderón’s inverse problem with a finite number of measurements. Forum Math. Sigma 7 (2019) e35. [Google Scholar]
  5. X. Antoine, H. Barucq and A. Bendali, Bayliss–Turkel-like radiation conditions on surfaces of arbitrary shape. J. Math. Anal. App. 229 (1999) 184–211. [Google Scholar]
  6. H. Barucq, J. Chabassier, M. Duruflé, L. Gizon and M. Leguèbe, Atmospheric radiation boundary conditions for the Helmholtz equation. ESAIM: M2AN 52 (2018) 945–964. [CrossRef] [EDP Sciences] [Google Scholar]
  7. H. Barucq, F. Faucher and H. Pham, Outgoing solutions to the scalar wave equation in helioseismology. Research Report RR-9280, Inria Bordeaux Sud-Ouest; Project-Team Magique3D (2019). [Google Scholar]
  8. A. Bayliss, M. Gunzburger and E. Turkel, Boundary conditions for the numerical solution of elliptic equations in exterior regions. SIAM J. Appl. Math. 42 (1982) 430–451. [Google Scholar]
  9. H. Buchholz, The Confluent Hypergeometric Function: With Special Emphasis on its Applications. In Vol. 15. Springer Science & Business Media (2013). [Google Scholar]
  10. J. Christensen-Dalsgaard, W. Däppen, S. Ajukov, E. Anderson, H. Antia, S. Basu, V. Baturin, G. Berthomieu, B. Chaboyer, S. Chitre, A.N. Cox, P. Demarque, J. Donatowicz, W.A. Dziembowski, M. Gabriel, D.O. Gough, D.B. Guenther, J.A. Guzik, J.W. Harvey, F. Hill, G. Houdek, C.A. Iglesias, A.G. Kosovichev, J.W. Leibacher, P. Morel, C.R. Proffitt, J. Provost, J. Reiter, E.J. Rhodes Jr, F.J. Rogers, I.W. Roxburgh, M.J. Thompson and R.K. Ulrich, The current state of solar modeling. Science 272 (1996) 1286–1292. [Google Scholar]
  11. D. Colton and R. Kress, Inverse Acoustic and Electromagnetic Scattering Theory. In Vol. 93. Springer Science & Business Media (2012). [Google Scholar]
  12. J. Dereziński and S. Richard, On radial Schrödinger operators with a Coulomb potential. Ann. Henri Poincaré 19 (2018) 2869–2917. [Google Scholar]
  13. D. Fournier, M. Leguèbe, C.S. Hanson, L. Gizon, H. Barucq, J. Chabassier and M. Duruflé, Atmospheric-radiation boundary conditions for high-frequency waves in time-distance helioseismology. Astron. Astrophys. 608 (2017) A109. [Google Scholar]
  14. L. Gizon, A.C. Birch and H.C. Spruit, Local helioseismology: three-dimensional imaging of the solar interior. Ann. Rev. Astron. Astrophys. 48 (2010) 289–338. [Google Scholar]
  15. L. Gizon, H. Barucq, M. Duruflé, C.S. Hanson, M. Leguèbe, A.C. Birch, J. Chabassier, D. Fournier, T. Hohage and E. Papini, Computational helioseismology in the frequency domain: acoustic waves in axisymmetric solar models with flows. Astron. Astrophys. 600 (2017) A35. [Google Scholar]
  16. J. Guillot and K. Zizi, Perturbations of the Laplacian by Coulomb like potentials. In: Scattering Theory in Mathematical Physics. Springer (1974) 237–242. [Google Scholar]
  17. L. Hostler and R. Pratt, Coulomb Green’s function in closed form. Phys. Rev. Lett. 10 (1963) 469. [Google Scholar]
  18. M. Hull and G. Breit, Coulomb wave functions. In: Nuclear Reactions II: Theory/Kernreaktionen II: Theorie. Springer (1959) 408–465. [Google Scholar]
  19. F. Ihlenburg, Finite Element Analysis of Acoustic Scattering. Springer Science & Business Media 132 (1998). [Google Scholar]
  20. F. Johansson, Arb: efficient arbitrary-precision midpoint-radius interval arithmetic. IEEE Trans. Comput. 66 (2017) 1281–1292. [Google Scholar]
  21. F. Johansson, Computing hypergeometric functions rigorously. ACM Trans. Math. Softw. 45 (2019) 1–26. [Google Scholar]
  22. S.G. Krantz, Harmonic and Complex Analysis in Several Variables. Springer (2017). [Google Scholar]
  23. R. Leis, Initial Boundary Value Problems in Mathematical Physics. Courier Corporation (1986). [Google Scholar]
  24. R. Leis and G.F. Roach, An initial boundary-value problem for the Schrödinger equation with long-range potential. Proc. R. Soc. Lond. A 417 (1988) 353–362. [Google Scholar]
  25. W. Magnus, F. Oberhettinger and R.P. Soni, Formulas and theorems for the special functions of mathematical physics. Springer Science & Business Media 52 (2013). [Google Scholar]
  26. N. Mandache, Exponential instability in an inverse problem for the Schrödinger equation. Inverse Prob. 17 (2001) 1435. [Google Scholar]
  27. P. Martin, Acoustic scattering by inhomogeneous spheres. J. Acoust. Soc. Am. 111 (2002) 2013–2018. [PubMed] [Google Scholar]
  28. A.I. Nachman, Global uniqueness for a two-dimensional inverse boundary value problem. Ann. Math. 143 (1996) 71–96. [Google Scholar]
  29. F. Olver, On the asymptotic solution of second-order differential equations having an irregular singularity of rank one, with an application to Whittaker functions. J. Soc. Ind. Appl. Math. Ser. B: Numer. Anal. 2 (1965) 225–243. [Google Scholar]
  30. F.W. Olver, D.W. Lozier, R.F. Boisvert and C.W. Clark, NIST Handbook of Mathematical Functions Hardback and CD-ROM. Cambridge University Press (2010). [Google Scholar]
  31. A. Ruiz, Harmonic analysis and inverse problems. Lectures Notes (2002). [Google Scholar]
  32. P. Stefanov, Scattering, Inverse Scattering and Resonances in ℝn (2019). [Google Scholar]
  33. G. Teschl, Mathematical methods in quantum mechanics. In Vol. 99 of Graduate Studies in Mathematics. American Mathematical Society (2009). [Google Scholar]
  34. D. Yafaev, Mathematical Scattering Theory: Analytic Theory. American Mathematical Society (2010). [Google Scholar]
  35. M. Zubeldia, Limiting absorption principle for the electromagnetic Helmholtz equation with singular potentials. Proc. R. Soc. Edinburgh Sect. A: Math. 144 (2014) 857–890. [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.

Recommended for you