LEADER 04476nam 22006615 450 001 9910742500203321 005 20240619100034.0 010 $a3-031-28288-4 024 7 $a10.1007/978-3-031-28288-1 035 $a(CKB)27451878700041 035 $a(MiAaPQ)EBC30620516 035 $a(Au-PeEL)EBL30620516 035 $a(DE-He213)978-3-031-28288-1 035 $a(PPN)272250589 035 $a(MiAaPQ)EBC30614491 035 $a(Au-PeEL)EBL30614491 035 $a(EXLCZ)9927451878700041 100 $a20230701d2023 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aMore Explorations in Complex Functions /$fby Richard Beals, Roderick S.C. Wong 205 $a1st ed. 2023. 210 1$aCham :$cSpringer Nature Switzerland :$cImprint: Springer,$d2023. 215 $a1 online resource (410 pages) 225 1 $aGraduate Texts in Mathematics,$x2197-5612 ;$v298 311 $a9783031282874 327 $a1. Basics -- 2. Further preliminaries -- 3. Complex dynamics -- 4. Univalent functions and de Brange's theorem -- 5. Harmonic and subharmonic functions; the Dirichlet problem -- 6. General Riemann surfaces -- 7. The uniformization theorem -- 8. Quasiconformal mapping -- 9. Introduction to Teichmüller theory -- 10. The Bergman kernel -- 11. Theta functions -- 12. Padé approximants and continued fractions -- 13. Riemann?Hilbert problems -- 14. Asymptotic and Darboux's method -- References -- Index. 330 $aMore Explorations in Complex Functions is something of a sequel to GTM 287, Explorations in Complex Functions. Both texts introduce a variety of topics, from core material in the mainstream of complex analysis to tools that are widely used in other areas of mathematics and applications, but there is minimal overlap between the two books. The intended readership is the same, namely graduate students and researchers in complex analysis, independent readers, seminar attendees, or instructors for a second course in complex analysis. Instructors will appreciate the many options for constructing a second course that builds on a standard first course in complex analysis. Exercises complement the results throughout. There is more material in this present text than one could expect to cover in a year?s course in complex analysis. A mapping of dependence relations among chapters enables instructors and independent readers a choice of pathway to reading the text. Chapters 2, 4, 5, 7, and 8 contain the function theory background for some stochastic equations of current interest, such as SLE. The text begins with two introductory chapters to be used as a resource. Chapters 3 and 4 are stand-alone introductions to complex dynamics and to univalent function theory, including deBrange?s theorem, respectively. Chapters 5?7 may be treated as a unit that leads from harmonic functions to covering surfaces to the uniformization theorem and Fuchsian groups. Chapter 8 is a stand-alone treatment of quasiconformal mapping that paves the way for Chapter 9, an introduction to Teichmüller theory. The final chapters, 10?14, are largely stand-alone introductions to topics of both theoretical and applied interest: the Bergman kernel, theta functions and Jacobi inversion, Padé approximants and continued fractions, the Riemann?Hilbert problem and integral equations, and Darboux?s method for computing asymptotics. 410 0$aGraduate Texts in Mathematics,$x2197-5612 ;$v298 606 $aFunctions of complex variables 606 $aFunctions, Special 606 $aNumber theory 606 $aFunctions of a Complex Variable 606 $aSpecial Functions 606 $aNumber Theory 606 $aFuncions de diverses variables complexes$2thub 608 $aLlibres electrònics$2thub 615 0$aFunctions of complex variables. 615 0$aFunctions, Special. 615 0$aNumber theory. 615 14$aFunctions of a Complex Variable. 615 24$aSpecial Functions. 615 24$aNumber Theory. 615 7$aFuncions de diverses variables complexes 676 $a515.9 676 $a515.9 700 $aBeals$b Richard$027941 701 $aWong$b Roderick S. C$01252016 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910742500203321 996 $aMore Explorations in Complex Functions$93556407 997 $aUNINA