03231nam 22005535 450 991030966370332120251113195259.03-030-03074-110.1007/978-3-030-03074-2(CKB)4100000007389672(DE-He213)978-3-030-03074-2(MiAaPQ)EBC5629357(PPN)233798641(EXLCZ)99410000000738967220190104d2018 u| 0engurnn#008mamaatxtrdacontentcrdamediacrrdacarrierSpectral Theory on the S-Spectrum for Quaternionic Operators /by Fabrizio Colombo, Jonathan Gantner, David P. Kimsey1st ed. 2018.Cham :Springer International Publishing :Imprint: Birkhäuser,2018.1 online resource (IX, 356 p.)Operator Theory: Advances and Applications,2296-4878 ;2703-030-03073-3 Introduction -- Slice hyperholomorphic functions -- The S-spectrum and the S-functional calculus -- Properties of the S-functional calculus for bounded operators -- The S-functional calculus for unbounded operators -- The H1 functional calculus -- The F-functional calculus for bounded operators -- The F-functional calculus for unbounded operators -- Quaternionic operators on a Hilbert space -- Spectral integrals -- The spectral theorem for bounded normal operators -- The spectral theorem for unbounded normal operators -- Spectral theorem for unitary operators -- Spectral Integration in the Quaternionic Setting -- Bounded Quaternionic Spectral Operators.The subject of this monograph is the quaternionic spectral theory based on the notion of S-spectrum. With the purpose of giving a systematic and self-contained treatment of this theory that has been developed in the last decade, the book features topics like the S-functional calculus, the F-functional calculus, the quaternionic spectral theorem, spectral integration and spectral operators in the quaternionic setting. These topics are based on the notion of S-spectrum of a quaternionic linear operator. Further developments of this theory lead to applications in fractional diffusion and evolution problems that will be covered in a separate monograph.Operator Theory: Advances and Applications,2296-4878 ;270Operator theoryDynamical systemsFunctional analysisOperator TheoryDynamical SystemsFunctional AnalysisOperator theory.Dynamical systems.Functional analysis.Operator Theory.Dynamical Systems.Functional Analysis.515.724Colombo Fabrizioauthttp://id.loc.gov/vocabulary/relators/aut511074Gantner Jonathanauthttp://id.loc.gov/vocabulary/relators/autKimsey David P.authttp://id.loc.gov/vocabulary/relators/autBOOK9910309663703321Spectral Theory on the S-Spectrum for Quaternionic Operators2017434UNINA