03825nam 2200721 450 991082752590332120230803204705.03-11-037783-73-11-031535-110.1515/9783110315356(CKB)3710000000229279(EBL)1663181(SSID)ssj0001332710(PQKBManifestationID)11876733(PQKBTitleCode)TC0001332710(PQKBWorkID)11377093(PQKB)11317521(MiAaPQ)EBC1663181(DE-B1597)209206(OCoLC)890071094(OCoLC)900717313(DE-B1597)9783110315356(Au-PeEL)EBL1663181(CaPaEBR)ebr11010157(CaONFJC)MIL805176(EXLCZ)99371000000022927920150211h20142014 uy 0engurnn#---|u||utxtccrThe D-bar Neumann problem and Schrödinger operators /Friedrich HaslingerBerlin, [Germany] ;Boston, [Massachusetts] :De Gruyter,2014.©20141 online resource (254 p.)De Gruyter Expositions in Mathematics,0938-6572 ;Volume 59Description based upon print version of record.3-11-031530-0 Includes bibliographical references and index.Front matter --Preface --Contents --1. Bergman spaces --2. The canonical solution operator to --3. Spectral properties of the canonical solution operator to --4. The complex --5. Density of smooth forms --6. The weighted complex --7. The twisted complex --8. Applications --9. Spectral analysis --10. Schrödinger operators and Witten-Laplacians --11. Compactness --12. The Neumann operator and the Bergman projection --13. Compact resolvents --14. Spectrum of on the Fock space --15. Obstructions to compactness --Bibliography --Index --BackmatterThe topic of this book is located at the intersection of complex analysis, operator theory and partial differential equations. It begins with results on the canonical solution operator to restricted to Bergman spaces of holomorphic d-bar functions in one and several complex variables. These operators are Hankel operators of special type. In the following the general complex is investigated on d-bar spaces over bounded pseudoconvex domains and on weighted d-bar spaces. The main part is devoted to the spectral analysis of the complex Laplacian and to compactness of the Neumann operator. The last part contains a detailed account of the application of the methods to Schrödinger operators, Pauli and Dirac operators and to Witten-Laplacians. It is assumed that the reader has a basic knowledge of complex analysis, functional analysis and topology. With minimal prerequisites required, this book provides a systematic introduction to an active area of research for both students at a bachelor level and mathematicians.De Gruyter expositions in mathematics ;Volume 59.Neumann problemSchrödinger operatorCompactness.Hankel Operator.Inhomogeneous Cauchy-Riemann Equation.Schrödinger Operator.Witten Laplacian.d-bar Neumann Problem.Neumann problem.Schrödinger operator.515/.9SK 620SEPArvkHaslinger Friedrich1141604MiAaPQMiAaPQMiAaPQBOOK9910827525903321The D-bar Neumann problem and Schrödinger operators4120115UNINA