The d-bar Neumann Problem and Schrödinger Operators

1 - Preface [Seite 7]
2 - Contents [Seite 9]
3 - 1 Bergman spaces [Seite 13]
3.1 - 1.1 Elementary properties [Seite 13]
3.2 - 1.2 Examples [Seite 20]
3.3 - 1.3 Biholomorphic maps [Seite 24]
3.4 - 1.4 Notes [Seite 27]
4 - 2 The canonical solution operator to ?? [Seite 28]
4.1 - 2.1 Compact operators on Hilbert spaces [Seite 28]
4.2 - 2.2 The canonical solution operator to [Seite 2.2 The canonical solution operator to]
.¯ restricted to A2(D) - 38 [Seite 38]
4.3 - 2.3 Notes [Seite 47]
5 - 3 Spectral properties of the canonical solution operator to [Seite 3 Spectral properties of the canonical solution operator to]
- 48 [Seite 48]
5.1 - 3.1 Complex differential forms [Seite 48]
5.2 - 3.2 (0, 1)-forms with holomorphic coefficients [Seite 49]
5.3 - 3.3 Compactness and Schatten class membership [Seite 51]
5.4 - 3.4 Notes [Seite 61]
6 - 4 The .¯ -complex [Seite 4 The .¯ -complex]
- 62 [Seite 62]
6.1 - 4.1 Unbounded operators on Hilbert spaces [Seite 62]
6.2 - 4.2 Distributions [Seite 77]
6.3 - 4.3 A finite-dimensional analog [Seite 83]
6.4 - 4.4 The .¯ -Neumann operator [Seite 4.4 The .¯ -Neumann operator]
- 84 [Seite 84]
6.5 - 4.5 Notes [Seite 98]
7 - 5 Density of smooth forms [Seite 99]
7.1 - 5.1 Friedrichs' Lemma and Sobolev spaces [Seite 99]
7.2 - 5.2 Density in the graph norm [Seite 110]
7.3 - 5.3 Notes [Seite 115]
8 - 6 The weighted .¯-complex [Seite 116]
8.1 - 6.1 The .¯-Neumann operator [Seite 6.1 The .¯-Neumann operator]
on (0, 1)-forms - 116 [Seite 116]
8.2 - 6.2 (0, q)-forms [Seite 6.2 (0, q)-forms]
- 121 [Seite 121]
8.3 - 6.3 Notes [Seite 124]
9 - 7 The twisted .¯-complex [Seite 7 The twisted .¯-complex]
- 126 [Seite 126]
9.1 - 7.1 An exact sequence of unbounded operators [Seite 126]
9.2 - 7.2 The twisted basic estimates [Seite 127]
9.3 - 7.3 Notes [Seite 130]
10 - 8 Applications [Seite 131]
10.1 - 8.1 Hörmander's L2-estimates [Seite 8.1 Hörmander's L2-estimates]
- 131 [Seite 131]
10.2 - 8.2 Weighted spaces of entire functions [Seite 134]
10.3 - 8.3 Notes [Seite 138]
11 - 9 Spectral analysis [Seite 139]
11.1 - 9.1 Resolutions of the identity [Seite 139]
11.2 - 9.2 Spectral decomposition of bounded normal operators [Seite 142]
11.3 - 9.3 Spectral decomposition of unbounded self-adjoint operators [Seite 148]
11.4 - 9.4 Determination of the spectrum [Seite 162]
11.5 - 9.5 Variational characterization of the discrete spectrum [Seite 172]
11.6 - 9.6 Notes [Seite 177]
12 - 10 Schrödinger operators and Witten-Laplacians [Seite 178]
12.1 - 10.1 Difference quotients [Seite 178]
12.2 - 10.2 Interior regularity [Seite 180]
12.3 - 10.3 Schrödinger operators with magnetic field [Seite 183]
12.4 - 10.4 Witten-Laplacians [Seite 190]
12.5 - 10.5 Dirac and Pauli operators [Seite 192]
12.6 - 10.6 Notes [Seite 194]
13 - 11 Compactness [Seite 195]
13.1 - 11.1 Precompact sets in L2-spaces [Seite 11.1 Precompact sets in L2-spaces]
- 195 [Seite 195]
13.2 - 11.2 Sobolev spaces and Gårding's inequality [Seite 198]
13.3 - 11.3 Compactness in weighted spaces [Seite 202]
13.4 - 11.4 Bounded pseudoconvex domains [Seite 214]
13.5 - 11.5 Notes [Seite 217]
14 - 12 The .¯-Neumann [Seite 12 The .¯-Neumann]
operator and the Bergman projection - 219 [Seite 219]
14.1 - 12.1 The Stone-Weierstraß Theorem [Seite 219]
14.2 - 12.2 Commutators of the Bergman projection [Seite 222]
14.3 - 12.3 Notes [Seite 227]
15 - 13 Compact resolvents [Seite 228]
15.1 - 13.1 Schrödinger operators [Seite 228]
15.2 - 13.2 Dirac and Pauli operators [Seite 230]
15.3 - 13.3 Notes [Seite 232]
16 - 14 Spectrum of . [Seite 14 Spectrum of .]
on the Fock space - 233 [Seite 233]
16.1 - 14.1 The general setting [Seite 233]
16.2 - 14.2 Determination of the spectrum [Seite 235]
16.3 - 14.3 Notes [Seite 240]
17 - 15 Obstructions to compactness [Seite 241]
17.1 - 15.1 The bidisc [Seite 241]
17.2 - 15.2 Weighted spaces [Seite 242]
17.3 - 15.3 Notes [Seite 246]
18 - Bibliography [Seite 247]
19 - Index [Seite 251]