A generalization of the radiation condition of Sommerfeld for N-body Schrödinger operators
Isozaki, Hiroshi
Journées équations aux dérivées partielles, (1993), p. 1-9 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU)
Publié le : 1993-01-01
@article{JEDP_1993____A11_0,
     author = {Isozaki, Hiroshi},
     title = {A generalization of the radiation condition of Sommerfeld for $N$-body Schr\"odinger operators},
     journal = {Journ\'ees \'equations aux d\'eriv\'ees partielles},
     year = {1993},
     pages = {1-9},
     mrnumber = {94f:81172},
     language = {en},
     url = {http://dml.mathdoc.fr/item/JEDP_1993____A11_0}
}

Isozaki, Hiroshi. A generalization of the radiation condition of Sommerfeld for $N$-body Schrödinger operators. Journées équations aux dérivées partielles,  (1993), pp. 1-9. http://gdmltest.u-ga.fr/item/JEDP_1993____A11_0/

[1] S. Agmon and L. Hörmander, Asymptotic properties of solutions of differential equations with simple characteristics, J. d'Anal. Math., 30 (1976), 1-38. | MR 57 #6776 | Zbl 0335.35013

[2] D.M. Eidus, The principle of limit amplitude, Russ. Math. Surveys, 24 (1969), 97-167. | MR 58 #29156 | Zbl 0197.08102

[3] C. Gérard, H. Isozaki and E. Skibsted, Commutator algebra and resolvent estimates, (preprint), (1993). | Zbl 0814.35086

[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. | Zbl 0174.14802

[5] T. Ikebe and Y. Saito, Limiting absorption method and absolute contnuity for the Schrödinger operator, J. Math. Kyoto Univ. 7 (1972), 513-542. | MR 47 #628 | Zbl 0257.35022

[6] H. Isozaki, Asymptotic properties of generalized eigenfunctions for three body Schrödinger operators, Commun. Math. Phys., 153 (1993), 1-21. | Zbl 0774.35064

[7] P. Perry, I.M. Sigal and B. Simon, Spectral analysis of N-body Schrödinger operators, Ann. Math. 114 (1981), 519-567. | MR 83b:81129 | Zbl 0477.35069

[8] F. Rellich, Über das asymptotische Verhalten der Lösungen von Δu + λu = 0 in unendlichen Gebieten, Jahresber. Deutch. Math. Verein., 53 (1943), 57-65. | MR 8,204c | Zbl 0028.16401

[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. | MR 43 #712 | Zbl 0218.35053

[10] A. Sommerfeld, Die Greensche Funktionen der Schwingungsgleichung, Jahresber. Deutch. Math. Verein., 21 (1912), 309-353. | JFM 43.0819.01

[11] B.R. Vainberg, Principles of radiation, limit absorption and limit amplitude, Russ. Math. Surveys, 21 (1966), 115-193. | MR 35 #4559 | Zbl 0172.13703

[12] I.N. Vekua, On metaharmonic functions, Trudy Mat. Inst. Akad. Nauk. Gruz. SSSR, 12 (1943), 105-174. | MR 6,123g | Zbl 0063.07996

[13] X.P. Wang, Micro-local resolvent estimates for N-body Schrödinger operators, preprint, Université de Nantes, 1992.