Preface -- Contents -- 1 Bergman spaces -- 1.1 Elementary properties -- 1.2 Examples -- 1.3 Biholomorphic maps -- 1.4 Notes -- 2 The canonical solution operator to ?? -- 2.1 Compact operators on Hilbert spaces -- 2.2 The canonical solution operator to ∂̄ restricted to A2(D) -- 2.3 Notes -- 3 Spectral properties of the canonical solution operator to -- 3.1 Complex differential forms -- 3.2 (0, 1)-forms with holomorphic coefficients -- 3.3 Compactness and Schatten class membership -- 3.4 Notes -- 4 The ∂̄ -complex -- 4.1 Unbounded operators on Hilbert spaces -- 4.2 Distributions -- 4.3 A finite-dimensional analog -- 4.4 The ∂̄ -Neumann operator -- 4.5 Notes -- 5 Density of smooth forms -- 5.1 Friedrichs' Lemma and Sobolev spaces -- 5.2 Density in the graph norm -- 5.3 Notes -- 6 The weighted ∂̄-complex -- 6.1 The ∂̄-Neumann operator on (0, 1)-forms -- 6.2 (0, q)-forms -- 6.3 Notes -- 7 The twisted ∂̄-complex -- 7.1 An exact sequence of unbounded operators -- 7.2 The twisted basic estimates -- 7.3 Notes -- 8 Applications -- 8.1 Hörmander's L2-estimates -- 8.2 Weighted spaces of entire functions -- 8.3 Notes -- 9 Spectral analysis -- 9.1 Resolutions of the identity -- 9.2 Spectral decomposition of bounded normal operators -- 9.3 Spectral decomposition of unbounded self-adjoint operators -- 9.4 Determination of the spectrum -- 9.5 Variational characterization of the discrete spectrum -- 9.6 Notes -- 10 Schrödinger operators and Witten-Laplacians -- 10.1 Difference quotients -- 10.2 Interior regularity -- 10.3 Schrödinger operators with magnetic field -- 10.4 Witten-Laplacians -- 10.5 Dirac and Pauli operators -- 10.6 Notes -- 11 Compactness -- 11.1 Precompact sets in L2-spaces -- 11.2 Sobolev spaces and Gårding's inequality -- 11.3 Compactness in weighted spaces -- 11.4 Bounded pseudoconvex domains -- 11.5 Notes.

12 The ∂̄-Neumann operator and the Bergman projection -- 12.1 The Stone-Weierstraß Theorem -- 12.2 Commutators of the Bergman projection -- 12.3 Notes -- 13 Compact resolvents -- 13.1 Schrödinger operators -- 13.2 Dirac and Pauli operators -- 13.3 Notes -- 14 Spectrum of ⃞ on the Fock space -- 14.1 The general setting -- 14.2 Determination of the spectrum -- 14.3 Notes -- 15 Obstructions to compactness -- 15.1 The bidisc -- 15.2 Weighted spaces -- 15.3 Notes -- Bibliography -- Index.