Classical Fine Potential Theory - 9789819604296

Classical Fine Potential TheoryAuthor(s): Mohamed El Kadiri, Bent Fuglede\nFormat: Hardback\nPublisher: Springer Nature Switzerland AG, Switzerland\nImprint: Springer Nature Switzerland AG\nISBN-13: 9789819604296, 978-9819604296\nSynopsis\nThis 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 ofR^n. These sets are defined relative to the coarsest topology onR^n, 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 e.