LEADER 05162nam 2200601 450 001 996483172603316 005 20230718113645.0 010 $a3-031-05296-X 035 $a(MiAaPQ)EBC7052881 035 $a(Au-PeEL)EBL7052881 035 $a(CKB)24286023400041 035 $a(PPN)263896986 035 $a(EXLCZ)9924286023400041 100 $a20230106h20222022 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aConvolution-like structures, differential operators and diffusion processes /$fRu?ben Sousa, Manuel Guerra, Semyon Yakubovich 210 1$aCham, Switzerland :$cSpringer,$d[2022] 210 4$d©2022 215 $a1 online resource (269 pages) 225 1 $aLecture notes in mathematics ;$vVolume 2315 311 08$aPrint version: Sousa, Rúben Convolution-Like Structures, Differential Operators and Diffusion Processes Cham : Springer International Publishing AG,c2022 9783031052958 320 $aIncludes bibliographical references and index. 327 $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 -- 3.1 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 -- 3.7 Whittaker Convolution of Functions -- 3.7.1 Mapping Properties in the Spaces Lp(r?) -- 3.7.2 The Convolution Banach Algebra L?,? -- 3.8 Convolution-Type Integral Equations -- 4 Generalized Convolutions for Sturm-Liouville Operators -- 4.1 Known Results and Motivation -- 4.2 Laplace-Type Representation -- 4.3 The Existence Theorem for Sturm-Liouville Product Formulas -- 4.3.1 The Associated Hyperbolic Cauchy Problem -- 4.3.2 The Time-Shifted Product Formula -- 4.3.3 The Product Formula for w? as the Limit Case -- 4.4 Sturm-Liouville Transform of Measures -- 4.5 Sturm-Liouville Convolution of Measures -- 4.5.1 Infinite Divisibility and Lévy-Khintchine Type Representation -- 4.5.2 Convolution Semigroups. 327 $a4.5.3 Additive and Lévy Processes -- 4.6 Sturm-Liouville Hypergroups -- 4.6.1 The Nondegenerate Case -- 4.6.2 The Degenerate Case: Degenerate Hypergroups of Full Support -- 4.7 Harmonic Analysis on Lp Spaces -- 4.7.1 A Family of L1 Spaces -- 4.7.2 Application to Convolution-Type Integral Equations -- 5 Convolution-Like Structures on Multidimensional Spaces -- 5.1 Convolutions Associated with Conservative Strong Feller Semigroups -- 5.2 Nonexistence of Convolutions: Diffusion Processes on Bounded Domains -- 5.2.1 Special Cases and Numerical Examples -- 5.2.2 Some Auxiliary Results -- 5.2.3 Eigenfunction Expansions, Critical Points and Nonexistence Theorems -- 5.3 Nonexistence of Convolutions: One-Dimensional Diffusions -- 5.4 Families of Convolutions on Riemannian Structures with Cone-Like Metrics -- 5.4.1 The Eigenfunction Expansion of the Laplace-Beltrami Operator -- 5.4.2 Product Formulas and Convolutions -- 5.4.3 Infinitely Divisible Measures and Convolution Semigroups -- 5.4.4 Special Cases -- 5.4.5 Product Formulas and Convolutions Associated with Elliptic Operators on Subsets of R2 -- A Some Open Problems -- References -- Index. 410 0$aLecture notes in mathematics (Springer-Verlag) ;$vv. 2315. 606 $aConvolutions (Mathematics) 606 $aDifferential operators 606 $aDiffusion processes 606 $aConvolucions (Matemàtica)$2thub 606 $aOperadors diferencials$2thub 606 $aProcessos de difusió$2thub 608 $aLlibres electrònics$2thub 615 0$aConvolutions (Mathematics) 615 0$aDifferential operators. 615 0$aDiffusion processes. 615 7$aConvolucions (Matemàtica) 615 7$aOperadors diferencials 615 7$aProcessos de difusió 676 $a512.86 700 $aSousa$b Ru?ben$c(Mathematician),$01252162 702 $aGuerra$b Manuel$g(Manuel Cidraes Castro), 702 $aYakubovich$b S. B$g(Semen B.),$f1961- 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996483172603316 996 $aConvolution-like structures, differential operators and diffusion processes$92999680 997 $aUNISA LEADER 01931oam 2200445 a 450 001 9910698996903321 005 20090610090724.0 035 $a(CKB)5470000002397902 035 $a(OCoLC)314357259 035 $a(EXLCZ)995470000002397902 100 $a20090312d2009 ua 0 101 0 $aeng 135 $aurmn||||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aForest Service$b[electronic resource] $eemerging issues highlight the need to address persistent management challenges : testimony before the Subcommittee on Interior, Environment, and Related Agencies, Committee on Appropriations, House of Representatives /$fstatement of Robin M. Nazzaro 210 1$a[Washington, D.C.] :$cU.S. Govt. Accountability Office,$d[2009] 215 $a18 pages $cdigital, PDF file 225 1 $aTestimony ;$vGAO-09-443T 300 $aTitle from title screen (viewed on Mar. 12, 2009). 300 $a"For release ... March 11, 2009." 320 $aIncludes bibliographical references. 330 $a[Testimony focuses on Forest Service] management challenges in three key areas: (1) wildland fire management, (2) data on program activities and costs, and (3) financial and performance accountability. 517 $aForest Service 606 $aForest reserves$zUnited States$xManagement 606 $aPublic lands$zUnited States$xManagement 615 0$aForest reserves$xManagement. 615 0$aPublic lands$xManagement. 700 $aNazzaro$b Robin M$01380853 712 02$aUnited States.$bCongress.$bHouse.$bCommittee on Appropriations.$bSubcommittee on Interior, Environment, and Related Agencies. 712 02$aUnited States.$bGovernment Accountability Office. 801 0$bEJB 801 1$bEJB 801 2$bESR 801 2$bGPO 906 $aBOOK 912 $a9910698996903321 996 $aForest Service$93429582 997 $aUNINA