A generalization of the radiation condition of Sommerfeld for N -body Schrödinger operators

Hiroshi Isozaki

Journées équations aux dérivées partielles (1993)

  • Volume: 1993, Issue: 11, page 1-9
  • ISSN: 0752-0360

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Isozaki, Hiroshi. "A generalization of the radiation condition of Sommerfeld for $N$-body Schrödinger operators." Journées équations aux dérivées partielles 1993.11 (1993): 1-9. <http://eudml.org/doc/93262>.

@article{Isozaki1993,
author = {Isozaki, Hiroshi},
journal = {Journées équations aux dérivées partielles},
keywords = {Schrödinger operator; microlocal methods; -body problem; Sommerfeld radiation condition},
language = {eng},
number = {11},
pages = {1-9},
publisher = {Ecole polytechnique},
title = {A generalization of the radiation condition of Sommerfeld for $N$-body Schrödinger operators},
url = {http://eudml.org/doc/93262},
volume = {1993},
year = {1993},
}

TY - JOUR
AU - Isozaki, Hiroshi
TI - A generalization of the radiation condition of Sommerfeld for $N$-body Schrödinger operators
JO - Journées équations aux dérivées partielles
PY - 1993
PB - Ecole polytechnique
VL - 1993
IS - 11
SP - 1
EP - 9
LA - eng
KW - Schrödinger operator; microlocal methods; -body problem; Sommerfeld radiation condition
UR - http://eudml.org/doc/93262
ER -

References

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  1. [1] S. Agmon and L. Hörmander, Asymptotic properties of solutions of differential equations with simple characteristics, J. d'Anal. Math., 30 (1976), 1-38. Zbl0335.35013MR57 #6776
  2. [2] D.M. Eidus, The principle of limit amplitude, Russ. Math. Surveys, 24 (1969), 97-167. Zbl0197.08102MR58 #29156
  3. [3] C. Gérard, H. Isozaki and E. Skibsted, Commutator algebra and resolvent estimates, (preprint), (1993). Zbl0814.35086
  4. [4] V.V. Grushin, On Sommerfeld type conditions for a certain class of partial differential equations, A.M.S. Transl. Ser. 2. 51 (1966), 82-112. Zbl0174.14802
  5. [5] T. Ikebe and Y. Saito, Limiting absorption method and absolute contnuity for the Schrödinger operator, J. Math. Kyoto Univ. 7 (1972), 513-542. Zbl0257.35022MR47 #628
  6. [6] H. Isozaki, Asymptotic properties of generalized eigenfunctions for three body Schrödinger operators, Commun. Math. Phys., 153 (1993), 1-21. Zbl0774.35064
  7. [7] P. Perry, I.M. Sigal and B. Simon, Spectral analysis of N-body Schrödinger operators, Ann. Math. 114 (1981), 519-567. Zbl0477.35069MR83b:81129
  8. [8] F. Rellich, Über das asymptotische Verhalten der Lösungen von Δu + λu = 0 in unendlichen Gebieten, Jahresber. Deutch. Math. Verein., 53 (1943), 57-65. Zbl0028.16401MR8,204c
  9. [9] J.R. Schulenberger and C.H. Wilcox, A Rellich uniqueness theorem for steady state wave propagation in inhomogeneous anisotropic media, Arch. Rational Mech. Anal. 41 (1971), 18-45. Zbl0218.35053MR43 #712
  10. [10] A. Sommerfeld, Die Greensche Funktionen der Schwingungsgleichung, Jahresber. Deutch. Math. Verein., 21 (1912), 309-353. Zbl43.0819.01JFM43.0819.01
  11. [11] B.R. Vainberg, Principles of radiation, limit absorption and limit amplitude, Russ. Math. Surveys, 21 (1966), 115-193. Zbl0172.13703MR35 #4559
  12. [12] I.N. Vekua, On metaharmonic functions, Trudy Mat. Inst. Akad. Nauk. Gruz. SSSR, 12 (1943), 105-174. Zbl0063.07996MR6,123g
  13. [13] X.P. Wang, Micro-local resolvent estimates for N-body Schrödinger operators, preprint, Université de Nantes, 1992. 

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