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001448484 001__ 1448484
001448484 003__ OCoLC
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001448484 019__ $$a1337855717
001448484 020__ $$a9783031052965$$q(electronic bk.)
001448484 020__ $$a303105296X$$q(electronic bk.)
001448484 020__ $$z9783031052958
001448484 020__ $$z3031052951
001448484 0247_ $$a10.1007/978-3-031-05296-5$$2doi
001448484 035__ $$aSP(OCoLC)1337943487
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001448484 049__ $$aISEA
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001448484 08204 $$a515/.43$$223/eng/20220805
001448484 1001_ $$aSousa, Rúben$$c(Mathematician)
001448484 24510 $$aConvolution-like structures, differential operators and diffusion processes /$$cRúben Sousa, Manuel Guerra, Semyon Yakubovich.
001448484 260__ $$aCham :$$bSpringer,$$c2022.
001448484 300__ $$a1 online resource (269 pages)
001448484 336__ $$atext$$btxt$$2rdacontent
001448484 337__ $$acomputer$$bc$$2rdamedia
001448484 338__ $$aonline resource$$bcr$$2rdacarrier
001448484 4901_ $$aLecture Notes in Mathematics ;$$vv. 2315
001448484 500__ $$a5.4.5 Product Formulas and Convolutions Associated with Elliptic Operators on Subsets of R2
001448484 5050_ $$6880-01$$aIntro -- Preface -- Contents -- List of Symbols -- 1 Introduction -- 1.1 Motivation and Scope -- 1.2 Organization of the Book -- 2 Preliminaries -- 2.1 Continuous-Time Markov Processes -- 2.2 Sturm-Liouville Theory -- 2.2.1 Solutions of the Sturm-Liouville Equation -- 2.2.2 Eigenfunction Expansions -- 2.2.3 Diffusion Semigroups Generated by Sturm-Liouville Operators -- 2.2.4 Remarkable Particular Cases -- 2.3 Generalized Convolutions and Hypergroups -- 2.4 Harmonic Analysis with Respect to the Kingman Convolution -- 3 The Whittaker Convolution
001448484 5058_ $$a3.1 A Special Case: The Kontorovich-Lebedev Convolution -- 3.2 The Product Formula for the Whittaker Function -- 3.3 Whittaker Translation -- 3.4 Index Whittaker Transforms -- 3.5 Whittaker Convolution of Measures -- 3.5.1 Infinitely Divisible Distributions -- 3.5.2 Lévy-Khintchine Type Representation -- 3.6 Lévy Processes with Respect to the Whittaker Convolution -- 3.6.1 Convolution Semigroups -- 3.6.2 Lévy and Gaussian Processes -- 3.6.3 Some Auxiliary Results on the Whittaker Translation -- 3.6.4 Moment Functions -- 3.6.5 Lévy-Type Characterization of the Shiryaev Process
001448484 5058_ $$a4.5 Sturm-Liouville Convolution of Measures -- 4.5.1 Infinite Divisibility and Lévy-Khintchine Type Representation -- 4.5.2 Convolution Semigroups -- 4.5.3 Additive and Lévy Processes -- 4.6 Sturm-Liouville Hypergroups -- 4.6.1 The Nondegenerate Case -- 4.6.2 The Degenerate Case: Degenerate Hypergroups of Full Support -- 4.7 Harmonic Analysis on Lp Spaces -- 4.7.1 A Family of L1 Spaces -- 4.7.2 Application to Convolution-Type Integral Equations -- 5 Convolution-Like Structures on Multidimensional Spaces -- 5.1 Convolutions Associated with Conservative Strong Feller Semigroups
001448484 5058_ $$a5.2 Nonexistence of Convolutions: Diffusion Processes on Bounded Domains -- 5.2.1 Special Cases and Numerical Examples -- 5.2.2 Some Auxiliary Results -- 5.2.3 Eigenfunction Expansions, Critical Points and Nonexistence Theorems -- 5.3 Nonexistence of Convolutions: One-Dimensional Diffusions -- 5.4 Families of Convolutions on Riemannian Structures with Cone-Like Metrics -- 5.4.1 The Eigenfunction Expansion of the Laplace-Beltrami Operator -- 5.4.2 Product Formulas and Convolutions -- 5.4.3 Infinitely Divisible Measures and Convolution Semigroups -- 5.4.4 Special Cases
001448484 506__ $$aAccess limited to authorized users.
001448484 520__ $$aThis book provides an introduction to recent developments in the theory of generalized harmonic analysis and its applications. It is well known that convolutions, differential operators and diffusion processes are interconnected: the ordinary convolution commutes with the Laplacian, and the law of Brownian motion has a convolution semigroup property with respect to the ordinary convolution. Seeking to generalize this useful connection, and also motivated by its probabilistic applications, the book focuses on the following question: given a diffusion process Xt on a metric space E, can we construct a convolution-like operator * on the space of probability measures on E with respect to which the law of Xt has the *-convolution semigroup property? A detailed analysis highlights the connection between the construction of convolution-like structures and disciplines such as stochastic processes, ordinary and partial differential equations, spectral theory, special functions and integral transforms. The book will be valuable for graduate students and researchers interested in the intersections between harmonic analysis, probability theory and differential equations.
001448484 588__ $$aOnline resource; title from PDF title page (SpringerLink, viewed August 5, 2022).
001448484 650_0 $$aConvolutions (Mathematics)
001448484 650_0 $$aDifferential operators.
001448484 650_0 $$aDiffusion processes.
001448484 655_0 $$aElectronic books.
001448484 655_7 $$aLlibres electrònics.$$2thub
001448484 7001_ $$aGuerra, Manuel.
001448484 7001_ $$aYakubovich, S. B.$$q(Semen B.),$$d1961-
001448484 77608 $$iPrint version:$$aSousa, Rúben$$tConvolution-Like Structures, Differential Operators and Diffusion Processes$$dCham : Springer International Publishing AG,c2022$$z9783031052958
001448484 830_0 $$aLecture notes in mathematics (Springer-Verlag) ;$$vv. 2315.
001448484 852__ $$bebk
001448484 85640 $$3Springer Nature$$uhttps://univsouthin.idm.oclc.org/login?url=https://link.springer.com/10.1007/978-3-031-05296-5$$zOnline Access$$91397441.1
001448484 909CO $$ooai:library.usi.edu:1448484$$pGLOBAL_SET
001448484 980__ $$aBIB
001448484 980__ $$aEBOOK
001448484 982__ $$aEbook
001448484 983__ $$aOnline
001448484 994__ $$a92$$bISE