Dissertationes mathematicae. 469: Complex absorbing potential method for systems / J.Kungsman, M.Melgaard; Institute of Mathematics. Polish Academy of Sciences. - Warszawa: Instytut matematyczny PAN, 2010. - 58 p.: ill. - Ref.: p.55-58. - ISSN 0012-3862  Место хранения:   013 | Институт математики СО РАН | Новосибирск | Библиотека

Оглавление / Contents

1 Introduction ................................................. 5 2 Preliminaries ................................................ 9 3 Matrix valued pseudodifferential operators .................. 10 3.1 Operators and symbols .................................. 10 3.2 Asymptotic series ...................................... 12 3.3 Inverses ............................................... 13 3.4 Semiclassical wavefront set ............................ 13 3.5 Helffer-Robert-Sjöstrand calculus ...................... 14 4 Framework and assumptions ................................... 14 4.1 Matrix valued black box framework ...................... 14 4.2 Complex scaling ........................................ 15 4.3 Resonances and resonant states ......................... 16 4.4 Reference operator ..................................... 17 5 Results ..................................................... 18 5.1 Individual resonances. The case R'0 < R1 ............... 18 5.2 Individual resonances. The case R1 < R'0 ............... 18 5.3 Clusters of resonances. The case R'0 < R1 .............. 19 5.4 Clusters of resonances. The case R1 < R'0 .............. 20 6 Cutoff resolvent estimate ................................... 20 7 Hamiltonians with complex absorbing potentials .............. 24 8 Eigenvalue estimate on a rectangle .......................... 28 9 Quasimodes .................................................. 31 10 Individual resonances. The case R'0 < Ri .................... 34 11 Individual resonances. The case R1 < R'0 .................... 37 12 Clusters of resonances ...................................... 41 A Auxiliary results ........................................... 50 A.l. Meromorphic extension .................................. 50 A.2. Properties of reference operator ....................... 51 B Operator valued semiclassical maximum principle ............. 52 References ..................................................... 55