標(biāo)題: Titlebook: Classical Potential Theory and Its Probabilistic Counterpart; Advanced Problems J. L. Doob Book 1984 Springer-Verlag New York Inc. 1984 Mar [打印本頁] 作者: NERVE 時(shí)間: 2025-3-21 17:23
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書目名稱Classical Potential Theory and Its Probabilistic Counterpart讀者反饋學(xué)科排名
作者: frenzy 時(shí)間: 2025-3-21 23:21 作者: 華而不實(shí) 時(shí)間: 2025-3-22 01:46
The Fine Topologyn . is said to be . than .) if . ? .. For any family of extended real-valued functions on a space there is a coarsest topology making every member of the family continuous, namely, the intersection of all the topologies doing this. The . topology of classical potential theory is defined as the coars作者: concise 時(shí)間: 2025-3-22 05:23
Classical Energy and Capacityductor, if . is a connected conducting body in ?., the charge on A distributes itself in such a way that the net effect is that of an all-positive or all-negative charge, and the distribution on . is in equilibrium in the sense that the restriction to . of the potential of the charge distribution in作者: 小蟲 時(shí)間: 2025-3-22 11:53 作者: Guileless 時(shí)間: 2025-3-22 14:52
Parabolic Potential Theory: Basic Factst operator . and its adjoint ., called ., will be developed in Chapters XV to XIX. Concepts that are parabolic counterparts of classical concepts will be distinguished by dots or asterisks, depending on whether the concepts are related to . or to .. Just as the domains of classical potential theory 作者: Guileless 時(shí)間: 2025-3-22 19:44 作者: originality 時(shí)間: 2025-3-22 22:40 作者: 乏味 時(shí)間: 2025-3-23 03:30
The Parabolic Dirichlet Problem, Sweeping, and Exceptional Setsabolic if . is parabolic, superparabolic, or sub-parabolic, respectively. The notation will be parallel to that in the classical context, with . omitted when .. Thus .,... need no further identification. In the dual context in which . is coparabolic we write 作者: 叫喊 時(shí)間: 2025-3-23 06:18
Classical Potential Theory and Its Probabilistic Counterpart978-1-4612-5208-5Series ISSN 0072-7830 Series E-ISSN 2196-9701 作者: 傲慢人 時(shí)間: 2025-3-23 12:29 作者: Thyroid-Gland 時(shí)間: 2025-3-23 14:37
https://doi.org/10.1007/978-1-4757-3049-4d the boundary of a subset of ?. is that relative to the compactification. In most of the discussion the nature of the boundary is irrelevant, and ?. can be taken, for example, as the Euclidean boundary or one-point boundary of ..作者: 窩轉(zhuǎn)脊椎動物 時(shí)間: 2025-3-23 20:00
https://doi.org/10.1007/978-1-4757-3803-2ductor, if . is a connected conducting body in ?., the charge on A distributes itself in such a way that the net effect is that of an all-positive or all-negative charge, and the distribution on . is in equilibrium in the sense that the restriction to . of the potential of the charge distribution in ?. is a constant function.作者: 可卡 時(shí)間: 2025-3-24 01:51
Dujuan Wang,Yunqiang Yin,Yaochu Jin is so elementary that it will be left to the reader to formulate and justify. A ball in ? with center ξ is an open interval with midpoint ξ, and the averages (., ξ, δ), .(., ξ, δ), and α. can play the same role when . = 1 as when . > 1, but more direct methods are sometimes clearer.作者: 清楚 時(shí)間: 2025-3-24 03:24 作者: chandel 時(shí)間: 2025-3-24 09:02
https://doi.org/10.1007/978-1-84882-474-4 there is one, is denoted by .. For example, if Г is a class of superparabolic functions and if Г has a subparabolic minorant then . exists and is parabolic. The proof is a translation of that of Theorem III.2. The corresponding notation in the coparabolic context is . and ..作者: ligature 時(shí)間: 2025-3-24 12:12 作者: 不適 時(shí)間: 2025-3-24 15:18
Polar Sets and Their Applicationst of the set in the neighborhood. An . set is a set whose compact subsets are polar. It will be shown in Section VI.2 that an analytic inner polar set is polar. If a set is (inner) polar its Kelvin transformsare also.作者: profligate 時(shí)間: 2025-3-24 22:29 作者: Discrete 時(shí)間: 2025-3-24 23:26
Classical Energy and Capacityductor, if . is a connected conducting body in ?., the charge on A distributes itself in such a way that the net effect is that of an all-positive or all-negative charge, and the distribution on . is in equilibrium in the sense that the restriction to . of the potential of the charge distribution in ?. is a constant function.作者: RENAL 時(shí)間: 2025-3-25 04:31 作者: 溝通 時(shí)間: 2025-3-25 10:16
Subparabolic, Superparabolic, and Parabolic Functions on a Slabregions. It is therefore to be expected from XV(7.3) that the upper boundary of . if . is a parabolic measure null set and that parabolic measure on the lower boundary is given by . so that if . is parabolic on . with boundary function . in some suitable sense on the lower boundary and if . is appropriately restricted, then 作者: Arthritis 時(shí)間: 2025-3-25 15:00 作者: obeisance 時(shí)間: 2025-3-25 17:51 作者: Clumsy 時(shí)間: 2025-3-25 20:11 作者: 豪華 時(shí)間: 2025-3-26 02:10
Estimating Population Parameters,Let . and if . denote by . the image of ξ under inversion in ?.. That is, . is on the ray from ξ. through ξ, and .. To simplify the notation take ..作者: 竊喜 時(shí)間: 2025-3-26 07:38 作者: 盡管 時(shí)間: 2025-3-26 11:03
Experimental Design and Analysis,Throughout this book a . subset of ?. is either a ball in ?. or ?. itself, but the latter only when . > 2. The Green function . for . a ball was defined in Section II.1. The Green function . for . = ?. with . > 2 is defined as .. If μ is a measure on a special open set ., define the function .μ on . by ..作者: 泛濫 時(shí)間: 2025-3-26 13:52
Experimental Design and Analysis,. . Г: . . ?., .(ξ) = inf..作者: aggressor 時(shí)間: 2025-3-26 17:40 作者: 十字架 時(shí)間: 2025-3-26 23:15
https://doi.org/10.1007/978-1-4757-3425-6The class of relative harmonic functions is suggested by the following trivial remark. Let (., .) be a measurable space, and suppose that to each point ξ of . is assigned some set (perhaps empty) . of probability measures on ..作者: ventilate 時(shí)間: 2025-3-27 04:28 作者: atopic-rhinitis 時(shí)間: 2025-3-27 07:44 作者: Venules 時(shí)間: 2025-3-27 11:55
Introduction to the Mathematical Background of Classical Potential TheoryIn this chapter some of the mathematical ideas of classical potential theory are introduced, under simplifying assumptions. The basic space is Euclidean . space ?.. For a ball . in ?..作者: thrombus 時(shí)間: 2025-3-27 14:44
Basic Properties of Harmonic, Subharmonic, and Superharmonic FunctionsLet . and if . denote by . the image of ξ under inversion in ?.. That is, . is on the ray from ξ. through ξ, and .. To simplify the notation take ..作者: ERUPT 時(shí)間: 2025-3-27 21:26 作者: 英寸 時(shí)間: 2025-3-28 00:22 作者: Explicate 時(shí)間: 2025-3-28 05:35 作者: FLIC 時(shí)間: 2025-3-28 09:13 作者: Mercurial 時(shí)間: 2025-3-28 10:52 作者: osculate 時(shí)間: 2025-3-28 15:25
Lattices and Related Classes of FunctionsIn this chapter certain function classes that arise naturally in potential theory will be discussed. These classes, the corresponding identically named classes in parabolic potential theory (Section XVIII.19) and in stochastic process theory (Chapter V of Part 2), are discussed together in Chapter I of Part 3.作者: 打擊 時(shí)間: 2025-3-28 19:21
The Martin BoundaryLet . be an open subset of ?.. If . is a ball, its Euclidean boundary is so well adapted to it from a potential theoretic point of view that the following statements are true.作者: palette 時(shí)間: 2025-3-29 00:57 作者: Priapism 時(shí)間: 2025-3-29 04:29 作者: STANT 時(shí)間: 2025-3-29 07:45 作者: sigmoid-colon 時(shí)間: 2025-3-29 14:16
https://doi.org/10.1007/0-8176-4444-Xt of the set in the neighborhood. An . set is a set whose compact subsets are polar. It will be shown in Section VI.2 that an analytic inner polar set is polar. If a set is (inner) polar its Kelvin transformsare also.作者: Allergic 時(shí)間: 2025-3-29 18:31 作者: 公共汽車 時(shí)間: 2025-3-29 22:18
Classification and Discrimination,n . is said to be . than .) if . ? .. For any family of extended real-valued functions on a space there is a coarsest topology making every member of the family continuous, namely, the intersection of all the topologies doing this. The . topology of classical potential theory is defined as the coars作者: 使長胖 時(shí)間: 2025-3-30 02:26
https://doi.org/10.1007/978-1-4757-3803-2ductor, if . is a connected conducting body in ?., the charge on A distributes itself in such a way that the net effect is that of an all-positive or all-negative charge, and the distribution on . is in equilibrium in the sense that the restriction to . of the potential of the charge distribution in作者: Afflict 時(shí)間: 2025-3-30 08:07 作者: Synapse 時(shí)間: 2025-3-30 09:04 作者: 卡死偷電 時(shí)間: 2025-3-30 12:37
On-Rubble Robot Systems for the DDT Project,regions. It is therefore to be expected from XV(7.3) that the upper boundary of . if . is a parabolic measure null set and that parabolic measure on the lower boundary is given by . so that if . is parabolic on . with boundary function . in some suitable sense on the lower boundary and if . is appro作者: GLIDE 時(shí)間: 2025-3-30 16:58
https://doi.org/10.1007/978-1-84882-474-4 there is one, is denoted by .. For example, if Г is a class of superparabolic functions and if Г has a subparabolic minorant then . exists and is parabolic. The proof is a translation of that of Theorem III.2. The corresponding notation in the coparabolic context is . and ..作者: accessory 時(shí)間: 2025-3-30 23:52
https://doi.org/10.1007/978-1-4020-8924-4abolic if . is parabolic, superparabolic, or sub-parabolic, respectively. The notation will be parallel to that in the classical context, with . omitted when .. Thus .,... need no further identification. In the dual context in which . is coparabolic we write 作者: Ophthalmoscope 時(shí)間: 2025-3-31 04:51 作者: Functional 時(shí)間: 2025-3-31 05:35
Dujuan Wang,Yunqiang Yin,Yaochu Jinare endpoints of continuous [strictly] downward-directed arcs from .. That is, . is [strictly] below . relative to . if and only if there is a continuous function . from [0,1] into . for which .(0) = .,/(1) = ., and ord . is a [strictly] decreasing function. The . [.] . of . is the set . and the . i作者: 相容 時(shí)間: 2025-3-31 13:14 作者: Aqueous-Humor 時(shí)間: 2025-3-31 17:08 作者: 慷慨不好 時(shí)間: 2025-3-31 20:17 作者: Badger 時(shí)間: 2025-4-1 01:36 作者: Factual 時(shí)間: 2025-4-1 03:53
Book 1984a Markov process can be used to define the Green function of a potential theory. Thus it is possible to define and develop many potential theoretic concepts probabilistically, a procedure potential theorists observe withjaun- diced eyes in view of the fact that now as in the past their subject provi作者: defendant 時(shí)間: 2025-4-1 06:31
Classification and Discrimination,y will be distinguished by an “f”, for example, f lim sup, δ.. From now on any otherwise unqualified topological concept will refer to the Euclidean topology. Since the fine topology is defined intrinsically in terms of superharmonic functions, it is not surprising that this topology plays a fundamental role in classical potential theory.作者: hemorrhage 時(shí)間: 2025-4-1 14:04
The Fine Topologyy will be distinguished by an “f”, for example, f lim sup, δ.. From now on any otherwise unqualified topological concept will refer to the Euclidean topology. Since the fine topology is defined intrinsically in terms of superharmonic functions, it is not surprising that this topology plays a fundamental role in classical potential theory.作者: Inculcate 時(shí)間: 2025-4-1 17:42
10樓作者: babble 時(shí)間: 2025-4-1 20:16
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