03604nam 2200649 450 991048104750332120170822144322.01-4704-0216-5(CKB)3360000000464811(EBL)3114561(SSID)ssj0000888835(PQKBManifestationID)11533779(PQKBTitleCode)TC0000888835(PQKBWorkID)10866991(PQKB)10224592(MiAaPQ)EBC3114561(PPN)195415116(EXLCZ)99336000000046481119971114h19981998 uy| 0engur|n|---|||||txtccrCombinatorial theory of the free product with amalgamation and operator-valued free probability theory /Roland SpeicherProvidence, Rhode Island :American Mathematical Society,[1998]©19981 online resource (105 p.)Memoirs of the American Mathematical Society,0065-9266 ;number 627"March 1998, volume 132, number 627 (third of 5 numbers)."0-8218-0693-9 Includes bibliographical references.""Contents""; ""Introduction""; ""Chapter I. Preliminaries on non-crossing partitions""; ""1.1. Non-crossing partitions""; ""1.2. Incidence algebra and convolution""; ""1.3. Multiplicative functions""; ""Chapter II. Operator-valued multiplicative functions on the lattice of non-crossing partitions""; ""2.1. Operator-valued multiplicative functions""; ""2.2. Connection between f and f â??C""; ""2.3. Special case I = I(C,C)""; ""2.4. Tracial multiplicative functions""; ""2.5. Product and cluster property""; ""Chapter III. Amalgamated free products""; ""3.1. Basic notations""""3.2. Moment and cumulant functions""""3.3. Definition of the amalgamated free product""; ""3.4. Explicit formula for α[sub(1)] â??α[sub(2)]""; ""3.5. Positivity of the amalgamated free product""; ""Chapter IV. Operator-valued free probability theory""; ""4.1. B-valued random variables and free convolution""; ""4.2. B-Gaussian distributions and central limit theorem""; ""4.3. Positivity of B-Gaussian distributions""; ""4.4. Compound B-Poisson distributions""; ""4.5. Infinitely divisible distributions""; ""4.6. Full Fock space over a Hilbert-B-bimodule""""4.7. Realization of infinitely divisible distributions on a full Fock space""""Chapter V. Operator-valued stochastic processes and stochastic differential equations""; ""5.1. B-valued stochastic processes""; ""5.2. Formulation of the problem""; ""5.3. Possible solutions of the problem""; ""5.4. Gaussian approximation""; ""Bibliography""Memoirs of the American Mathematical Society ;no. 627.Operator-valued functionsSelfadjoint operatorsFree products (Group theory)Combinatorial analysisFree probability theoryElectronic books.Operator-valued functions.Selfadjoint operators.Free products (Group theory)Combinatorial analysis.Free probability theory.510 s512/.55Speicher Roland1960-303453MiAaPQMiAaPQMiAaPQBOOK9910481047503321Combinatorial theory of the free product with amalgamation and operator-valued free probability theory2011511UNINA