LEADER 02915nam 2200493 450 001 9910536230203321 005 20230814221558.0 010 $a3-11-042615-3 024 7 $a10.1515/9783110417241 035 $a(CKB)4100000001044512 035 $a(MiAaPQ)EBC5158933 035 $a(DE-B1597)450203 035 $a(OCoLC)1013729242 035 $a(DE-B1597)9783110417241 035 $a(Au-PeEL)EBL5158933 035 $a(CaPaEBR)ebr11473980 035 $a(EXLCZ)994100000001044512 100 $a20171222h20182018 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $2rdacontent 182 $2rdamedia 183 $2rdacarrier 200 10$aComplex analysis $ea functional analytic approach /$fFriedrich Haslinger 210 1$aBerlin, [Germany] ;$aBoston, [Massachusetts] :$cDe Gruyter,$d2018. 210 4$d©2018 215 $a1 online resource (348 pages) $cillustrations 225 0 $aDe Gruyter Textbook 311 $a3-11-041723-5 311 $a3-11-041724-3 320 $aIncludes bibliographical references and index. 327 $tFrontmatter -- $tPreface -- $tContents -- $t1. Complex numbers and functions -- $t2. Cauchy's Theorem and Cauchy's formula -- $t3. Analytic continuation -- $t4. Construction and approximation of holomorphic functions -- $t5. Harmonic functions -- $t6. Several complex variables -- $t7. Bergman spaces -- $t8. The canonical solution operator to ?? -- $t9. Nuclear Fréchet spaces of holomorphic functions -- $t10. The ??-complex -- $t11. The twisted ??-complex and Schrödinger operators -- $tBibliography -- $tIndex 330 $aIn this textbook, a concise approach to complex analysis of one and several variables is presented. After an introduction of Cauchy's integral theorem general versions of Runge's approximation theorem and Mittag-Leffler's theorem are discussed. The fi rst part ends with an analytic characterization of simply connected domains. The second part is concerned with functional analytic methods: Fréchet and Hilbert spaces of holomorphic functions, the Bergman kernel, and unbounded operators on Hilbert spaces to tackle the theory of several variables, in particular the inhomogeneous Cauchy-Riemann equations and the d-bar Neumann operator. ContentsComplex numbers and functionsCauchy's Theorem and Cauchy's formulaAnalytic continuationConstruction and approximation of holomorphic functionsHarmonic functionsSeveral complex variablesBergman spacesThe canonical solution operator to Nuclear Fréchet spaces of holomorphic functionsThe -complexThe twisted -complex and Schrödinger operators 606 $aMathematics$vTextbooks 615 0$aMathematics 676 $a510 700 $aHaslinger$b Friedrich$01141604 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910536230203321 996 $aComplex analysis$92680057 997 $aUNINA