LEADER 03648nam 22006135 450 001 9910993932203321 005 20260126133106.0 010 $a981-9604-30-3 024 7 $a10.1007/978-981-96-0430-2 035 $a(CKB)38337775200041 035 $a(DE-He213)978-981-96-0430-2 035 $a(MiAaPQ)EBC32004071 035 $a(Au-PeEL)EBL32004071 035 $a(EXLCZ)9938337775200041 100 $a20250408d2025 u| 0 101 0 $aeng 135 $aur||||||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aClassical Fine Potential Theory /$fby Mohamed El Kadiri, Bent Fuglede 205 $a1st ed. 2025. 210 1$aSingapore :$cSpringer Nature Singapore :$cImprint: Springer,$d2025. 215 $a1 online resource (XVIII, 420 p. 2 illus., 1 illus. in color.) 225 1 $aSpringer Monographs in Mathematics,$x2196-9922 311 08$a981-9604-29-X 327 $aBackground in Potential Theory -- Fundamentals of Fine Potential Theory -- Further Developments -- Fine Complex Potential Theory. 330 $aThis comprehensive book explores the intricate realm of fine potential theory. Delving into the real theory, it navigates through harmonic and subharmonic functions, addressing the famed Dirichlet problem within finely open sets of Rn. These sets are defined relative to the coarsest topology on Rn, ensuring the continuity of all subharmonic functions. This theory underwent extensive scrutiny starting from the 1970s, particularly by Fuglede, within the classical or axiomatic framework of harmonic functions. The use of methods from fine potential theory has led to solutions of important classical problems and has allowed the discovery of elegant results for extension of classical holomorphic function to wider classes of ?domains?. Moreover, this book extends its reach to the notion of plurisubharmonic and holomorphic functions within plurifinely open sets of Cn and its applications to pluripotential theory. These open sets are defined by coarsest topology that renders all plurisubharmonic functions continuous on C^n. The presentation is meticulously crafted to be largely self-contained, ensuring accessibility for readers at various levels of familiarity with the subject matter. Whether delving into the fundamentals or seeking advanced insights, this book is an indispensable reference for anyone intrigued by potential theory and its myriad applications. Organized into five chapters, the first four unravel the intricacies of fine potential theory, while the fifth chapter delves into plurifine pluripotential theory. 410 0$aSpringer Monographs in Mathematics,$x2196-9922 606 $aPotential theory (Mathematics) 606 $aHarmonic analysis 606 $aTopology 606 $aPotential Theory 606 $aAbstract Harmonic Analysis 606 $aTopology 606 $aTeoria del potencial (Matemātica)$2thub 608 $aLlibres electrōnics$2thub 615 0$aPotential theory (Mathematics) 615 0$aHarmonic analysis. 615 0$aTopology. 615 14$aPotential Theory. 615 24$aAbstract Harmonic Analysis. 615 24$aTopology. 615 7$aTeoria del potencial (Matemātica) 676 $a515.96 700 $aQa?diri?$b Muh?ammad$4aut$4http://id.loc.gov/vocabulary/relators/aut$01887909 702 $aFuglede$b Bent$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910993932203321 996 $aClassical Fine Potential Theory$94526026 997 $aUNINA