03202nam 2200613 450 991081275160332120170816143258.01-4704-0387-0(CKB)3360000000464973(EBL)3114376(SSID)ssj0000973488(PQKBManifestationID)11504623(PQKBTitleCode)TC0000973488(PQKBWorkID)10984562(PQKB)11262749(MiAaPQ)EBC3114376(RPAM)13268628(PPN)195416759(EXLCZ)99336000000046497320030710d2003 uy| 0engur|n|---|||||txtccrPositive definite functions on infinite-dimensional convex cones /Helge GlöcknerProvidence, Rhode Island :American Mathematical Society,2003.1 online resource (150 p.)Memoirs of the American Mathematical Society,0065-9266 ;number 789"Volume 166, number 789 (second of 3 numbers)."0-8218-3256-5 Includes bibliographical references and index.""Contents""; ""Introduction""; ""Part I. Preliminaries and Preparatory Results""; ""1 Bounded and unbounded operators""; ""2 Cone-valued measures""; ""3 Measures on topological spaces""; ""4 Projective limits of cone-valued measures""; ""5 Holomorphic functions""; ""6 Involutive semigroups and their representations""; ""7 Positive definite kernels and functions""; ""8 C*-algebras associated with involutive semigroups""; ""9 Integral representations of positive definite functions""; ""10 Convex cones and their faces""; ""11 Examples of convex cones""""12 Conelike semigroups: definition and examples""""13 Representations of conelike semigroups I""; ""14 Fourier and Laplace transforms""; ""15 Generalized Bochner and Stone Theorems""; ""Part II. Main Results""; ""16 Nussbaum Theorem for open convex cones""; ""17 Positive definite functions on convex cones with non-empty interior""; ""18 Positive definite functions on convex sets""; ""19 Associated Hilbert spaces and representations""; ""20 Nussbaum Theorem for generating convex cones""; ""21 Representations of conelike semigroups II""; ""22 Associated unitary representations""""23 Holomorphic extension of unitary representations""""24 Holomorphic extension of representations of nuclear groups""; ""References""; ""Index""; ""List of Symbols""Memoirs of the American Mathematical Society ;no. 789.Harmonic analysisConvex bodiesRepresentations of groupsLaplace transformationHarmonic analysis.Convex bodies.Representations of groups.Laplace transformation.510 s515/.2433Glöckner Helge1969-1226MiAaPQMiAaPQMiAaPQBOOK9910812751603321Positive definite functions on infinite-dimensional convex cones3952131UNINA