Dissertationes mathematicae; 469 (Warszawa, 2010). - ОГЛАВЛЕНИЕ / CONTENTS
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ОбложкаDissertationes 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
 

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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


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