@incollection{AST_1992__210__183_0, author = {Hempel, Rainer}, title = {Eigenvalue asymptotics related to impurities in crystals}, booktitle = {M\'ethodes semi-classiques Volume 2 - Colloque international (Nantes, juin 1991)}, series = {Ast\'erisque}, pages = {183--196}, publisher = {Soci\'et\'e math\'ematique de France}, number = {210}, year = {1992}, language = {en}, url = {http://www.numdam.org/item/AST_1992__210__183_0/} }
TY - CHAP AU - Hempel, Rainer TI - Eigenvalue asymptotics related to impurities in crystals BT - Méthodes semi-classiques Volume 2 - Colloque international (Nantes, juin 1991) AU - Collectif T3 - Astérisque PY - 1992 SP - 183 EP - 196 IS - 210 PB - Société mathématique de France UR - http://www.numdam.org/item/AST_1992__210__183_0/ LA - en ID - AST_1992__210__183_0 ER -
%0 Book Section %A Hempel, Rainer %T Eigenvalue asymptotics related to impurities in crystals %B Méthodes semi-classiques Volume 2 - Colloque international (Nantes, juin 1991) %A Collectif %S Astérisque %D 1992 %P 183-196 %N 210 %I Société mathématique de France %U http://www.numdam.org/item/AST_1992__210__183_0/ %G en %F AST_1992__210__183_0
Hempel, Rainer. Eigenvalue asymptotics related to impurities in crystals, dans Méthodes semi-classiques Volume 2 - Colloque international (Nantes, juin 1991), Astérisque, no. 210 (1992), pp. 183-196. http://www.numdam.org/item/AST_1992__210__183_0/
[1] Eigenvalue branches of the Schrödinger operator in a spectral gap of . Commun. Math. Phys. 121 (1989), 291-321.
, and :[2] Existence of solutions for semilinear elliptic equations with indefinite linear part. Preprint, 1990.
and :[3] Solid State Physics. Holt, Rinehart and Winston, New York 1976.
and :[4] Discrete spectrum in the gaps of the continuous one in the large coupling constant limit. In : Operator Theory : Advance and Applications, Vol. 46. Birkhäuser, Basel 1990.
:[5] Spectral stability under tunneling. Commun. Math. Phys. 126 (1989), 133-156.
, and :[6] Methods of Mathematical Physics. Vol. I. Interscience, New York 1953.
and :[7] On the existence of eigenvalues of the Schrödinger operator in a gap of . Commun. Math. Phys. 103 (1986), 461-490.
and :[8] On the decoupling of finite singularities from the question of asymptotic completeness in two-body quantum systems. J. Funct. Anal. 23 (1976), 218-238.
and :[9] The spectral theory of periodic differential equations. Scottish Academic Press, Edinburgh 1973.
:[10] Trapping and cascading of eigenvalues in the large coupling limit. Commun. Math. Phys. 116 (1988), 597-634.
, , , , , and :[11] On a theorem of Deift and Hempel. Commun. Math. Phys. 116 (1988), 503-505.
and :[12] Introduction to the Theory of Linear Non-selfadjoint Operators. Amer. Math. Soc., Providence (R. I.) 1969.
and :[13] A left-indefinite generalized eigenvalue problem for Schrödinger operators. Habilitations schrift, Univ. München 1987.
:[14] On the asymptotic distribution of the eigenvalue branches of the Schrödinger operator in a spectral gap of . J. Reine Angew. Math. 399 (1989), 38-59.
:[15] Eigenvalues in gaps and decoupling by Neumann boundary conditions. J. Math. Anal. Appl., to appear.
:[16] Perturbation theory for linear operators. Springer, New York 1966.
:[17] Small perturbations and the eigenvalues of the Laplacian on large bounded domains. Proc. Amer. Math. Soc. 101 (1987), 509-512.
:[18] Some applications of the Birman-Schwinger principle. Helv. Phys. Acta 55 (1982), 49-68.
:[19] Impuretés dans une structure périodique. Journées " Équations aux dérivées partielles " (Saint Jean des Monts, 1990), Exp. No. XX, Ecole Polytech., Palaiseau, 1990
:[20] Comportement semi-classique pour l'opérateur de Schrödinger à potentiel périodique. J. Funct. Anal. 72 (1987), 65-93.
:[21] The electronic structure of impurities and other point defects in semiconductors. Rev. Mod. Phys. 50 (1978), 797-858.
:[22] Methods of modern mathematical physics. Vol. I. Functional Analysis. Revised and enlarged ed. Academic Press, New York 1981.
and :[23] Methods of modern mathematical physics. Vol. III. Scattering theory. Academic Press, New York 1979.
and :[24] Methods of modern mathematical physics. Vol. IV. Analysis of operators. Academic Press, New York 1978.
and :[25] Trace Ideals and their applications. Cambridge Univ. Press, London 1979.
:[26] A canonical decomposition for quadratic forms with application to monotone convergence theorems. J. Funct. Anal. 28 (1978), 377-385.
:[27] Stetige Abhängigkeit der Eigenwerte und Eigenfunktionen elliptischer Differentialoperatoren vom Gebiet. Math. Scand. 54 (1984), 51- 69.
:[28] The Weyl asymptotics for discrete spectrum of the perturbed Hill operator. Preprint, 1991
: