標(biāo)題: Titlebook: Complex Analysis; A Functional Analysi D. H. Luecking,L. A. Rubel Textbook 1984 Springer-Verlag New York Inc. 1984 Analysis.Funktionalanaly [打印本頁(yè)] 作者: CYNIC 時(shí)間: 2025-3-21 17:17
書(shū)目名稱Complex Analysis影響因子(影響力)
作者: 金桌活畫(huà)面 時(shí)間: 2025-3-21 20:47
Properties of ,(G) and ,(G),, G is an open set in ? × ? = ?.. Then .(G) is defined just as in the one-variable case. (The distance in ?. between two points (z,w) and (z’,w’) will be denoted d((z,w), (z’,w’)) = (|z - z’|. + |w - w’|.).. We also define .(G) as before, but must first define ..作者: orient 時(shí)間: 2025-3-22 03:18 作者: Camouflage 時(shí)間: 2025-3-22 08:18 作者: Coeval 時(shí)間: 2025-3-22 12:13
The Cauchy Theorem,rectifiable curve γ: [0,1] → ?, we let ‖γ‖ denote its length, i.e. ‖γ‖ = 1 |γ′(t)|dt, so that . where ‖f‖ = sup{| f(z) |: z ∈ γ}. The reader is reminded that γ^ denotes the “physical curve”, that is the image of γ.作者: Aprope 時(shí)間: 2025-3-22 16:31
Constructive Function Theory,n what follows, when we speak of a sequence of complex numbers we ordinarily mean a sequence with multiplicity, so that a function taking some value at a point of the sequence must take that value with the appropriate multiplicity. We also exclude the trivial function f ≡ 0 unless otherwise noted.作者: Aprope 時(shí)間: 2025-3-22 18:27
Ring (not Algebra) Isomorphisms of ,(G),s) = .(r) + .(s) for all r, s ∈ R.. A ring isomorphism is a ring homomorphism that is one-to-one and onto. If G and G’ are two conformally equivalent domains in ? then there is an algebra isomorphism from .(G) to .(G’) as we saw in Chapter 5. An algebra isomorphism will be a ring isomorphism which a作者: altruism 時(shí)間: 2025-3-22 23:13 作者: 嘴唇可修剪 時(shí)間: 2025-3-23 04:52
Gap-Interpolation Theorems,nd interpolation are mixed. The idea is to take the Germay interpolation situation, where we want f(z.) = w., n = 1,2,3,… for some entire function f but now require that f have the form . where ? is a given set of positive integers. For certain ? (like ? = ., the set of all positive integers), this 作者: 笨拙處理 時(shí)間: 2025-3-23 07:10
Textbook 1984m the point of view of functional analysis. The main object of study is the algebra H(G) of all holomorphic functions on the open set G, with the topology on H(G) of uniform convergence on compact subsets of G. From this point of vie~, the main theorem of the theory is Theorem 9.5, which concretely 作者: Cognizance 時(shí)間: 2025-3-23 10:51
https://doi.org/10.1007/978-3-642-97615-5dditionally preserves scalar multiplication. It follows from Proposition 5.4 that .(G) and .(G’) are isomorphic as algebras if and only if G and G’ are conformally equivalent. But a ring isomorphism can exist without conformal equivalence.作者: diskitis 時(shí)間: 2025-3-23 17:52 作者: 有限 時(shí)間: 2025-3-23 20:46
Christian Büning,Constantin Wirth(f) = ∫ f(z)dμ(z) when it is necessary to indicate the independent variable. “Measures” have the same properties as continuous linear functionals (which is what they are); for reinforcement, we list them here. Given μ ∈ M.(G):作者: Banister 時(shí)間: 2025-3-23 23:07
The Dual of ,(G),(f) = ∫ f(z)dμ(z) when it is necessary to indicate the independent variable. “Measures” have the same properties as continuous linear functionals (which is what they are); for reinforcement, we list them here. Given μ ∈ M.(G):作者: nullify 時(shí)間: 2025-3-24 06:00 作者: 菊花 時(shí)間: 2025-3-24 08:36
Interpolation,icit formula. The second is via solving infinitely many linear equations in infinitely many unknowns, the Taylor coefficients. (See [M. Eidelheit] and [P. J. Davis].) The third is via functional analysis—specifically the Banach-Dieudonné theorem. Kere we take the third route, obtaining in the process a functional analysis proof of Theorem 12.18.作者: Lineage 時(shí)間: 2025-3-24 14:32
0172-5939 erial, from the point of view of functional analysis. The main object of study is the algebra H(G) of all holomorphic functions on the open set G, with the topology on H(G) of uniform convergence on compact subsets of G. From this point of vie~, the main theorem of the theory is Theorem 9.5, which c作者: 防銹 時(shí)間: 2025-3-24 17:11 作者: 憤憤不平 時(shí)間: 2025-3-24 20:08 作者: 拒絕 時(shí)間: 2025-3-25 01:07
Complex Analysis978-1-4613-8295-9Series ISSN 0172-5939 Series E-ISSN 2191-6675 作者: paradigm 時(shí)間: 2025-3-25 04:12 作者: Nonthreatening 時(shí)間: 2025-3-25 11:09 作者: 使迷惑 時(shí)間: 2025-3-25 14:40 作者: 現(xiàn)暈光 時(shí)間: 2025-3-25 17:20 作者: 社團(tuán) 時(shí)間: 2025-3-25 21:42 作者: 天空 時(shí)間: 2025-3-26 01:15 作者: 最高峰 時(shí)間: 2025-3-26 05:17 作者: 使習(xí)慣于 時(shí)間: 2025-3-26 11:03 作者: Pandemic 時(shí)間: 2025-3-26 15:39
Sportswomen’s Apparel Around the World, G is an open set in ? × ? = ?.. Then .(G) is defined just as in the one-variable case. (The distance in ?. between two points (z,w) and (z’,w’) will be denoted d((z,w), (z’,w’)) = (|z - z’|. + |w - w’|.).. We also define .(G) as before, but must first define ..作者: 對(duì)手 時(shí)間: 2025-3-26 17:19
Sportswomen’s Apparel in the United Statesof seminorms. For each non-empty finite set A = {‖?‖., ‖?‖.,…, ‖?‖.} ? ., define., x ∈ E. Then ‖?‖. is a seminorm. Let . = . ∪ {‖?‖.: A is a non empty finite subset of .}; then . and . generate the same topology on E (Exercise 2). Consequently, we may assume . = . in the following proposition.作者: cartilage 時(shí)間: 2025-3-26 21:04 作者: triptans 時(shí)間: 2025-3-27 01:53 作者: ANN 時(shí)間: 2025-3-27 06:45
Shariman Ismadi Ismail,Uwe G. Kerstingn what follows, when we speak of a sequence of complex numbers we ordinarily mean a sequence with multiplicity, so that a function taking some value at a point of the sequence must take that value with the appropriate multiplicity. We also exclude the trivial function f ≡ 0 unless otherwise noted.作者: 跟隨 時(shí)間: 2025-3-27 09:33
https://doi.org/10.1007/978-3-642-97615-5s) = .(r) + .(s) for all r, s ∈ R.. A ring isomorphism is a ring homomorphism that is one-to-one and onto. If G and G’ are two conformally equivalent domains in ? then there is an algebra isomorphism from .(G) to .(G’) as we saw in Chapter 5. An algebra isomorphism will be a ring isomorphism which a作者: SAGE 時(shí)間: 2025-3-27 15:24
J?rn Littkemann,Sebastian Kleisty Theorem (12.14) says that there exists an entire function that interpolates given values at a given sequence of points. There are three major approaches that can be taken to proving such a theorem. The first is via the Mittag-Leffler Theorem and Weierstrass products, which involves writing an expl作者: 來(lái)自于 時(shí)間: 2025-3-27 20:13 作者: 中古 時(shí)間: 2025-3-28 00:37
Matilda Elfgaard,Anna Hafsteinsson ?stenbergOur goal is the treatment of complex analysis from the point of view of topological vector spaces. Here we present the basic definitions and some well-known facts.作者: 高談闊論 時(shí)間: 2025-3-28 04:25
Sportswomen’s Apparel in the United StatesIt is commonly prove in courses of advanced calculus that compact sets in . (or more generally .) are characterized by being closed and bounded. In a general topological vector space only one implication is correct. Here and in the future we will assume that our topological vector spaces are Hausdorff.作者: 最有利 時(shí)間: 2025-3-28 08:36
Sportswomen’s Apparel in the United StatesThe concept of duality is one of the most productive in analysis. One can very nearly characterize applications of functional analysis as applications of duality. Most of our goal in succeeding sections will be identifying the dual of .(G) and exploiting that identification. Toward this end, we begin with the definition.作者: 收集 時(shí)間: 2025-3-28 14:04
Emily Fairchild,Elizabeth A. GreggA major tool in the application of duality results (in . locally convex topological vector space) is the Hahn-Banach Theorem. We state here one standard version (there are many equivalent versions) and two important corollaries.作者: 精確 時(shí)間: 2025-3-28 16:10 作者: 秘密會(huì)議 時(shí)間: 2025-3-28 19:32
Christian Büning,Constantin WirthIf f ∈ .(G), G a connected open set, it is a consequence of the power series expansion for holomorphic functions that if f(z.) = 0, z. → z. ∈ G then f = 0 in G. It is also a consequence that if f.(z.) = 0 for n = 0,1,2,…, then f = 0 in G. We adopt conventions about “sets with multiplicity” that allow us to treat both cases as one.作者: CUR 時(shí)間: 2025-3-29 01:05
Erste Hilfe bei Sportverletzungen,We use the results of the previous section to derive some descriptive results on ideals of holomorphic functions.作者: 過(guò)去分詞 時(shí)間: 2025-3-29 05:47
Erste Hilfe bei Sportverletzungen,The Riemann Mapping Theorem implies that, as far as . can tell, all simply connected regions are the “same”. To clarify what this means we need the following notion of equivalence.作者: 法律 時(shí)間: 2025-3-29 09:23 作者: 無(wú)表情 時(shí)間: 2025-3-29 11:26
https://doi.org/10.1007/978-3-030-67249-2This chapter is intended as a prerequisite for later chapters. In it we introduce a topology on the dual of a topological vector space. We present some of the standard results in the theory of Fréchet spaces and some additional results on topological vector spaces in general.作者: 小教堂 時(shí)間: 2025-3-29 17:32 作者: Highbrow 時(shí)間: 2025-3-29 23:18 作者: OTTER 時(shí)間: 2025-3-30 02:47
Duality,The concept of duality is one of the most productive in analysis. One can very nearly characterize applications of functional analysis as applications of duality. Most of our goal in succeeding sections will be identifying the dual of .(G) and exploiting that identification. Toward this end, we begin with the definition.作者: 希望 時(shí)間: 2025-3-30 07:13
The Hahn-Banach Theorem, and Applications,A major tool in the application of duality results (in . locally convex topological vector space) is the Hahn-Banach Theorem. We state here one standard version (there are many equivalent versions) and two important corollaries.作者: 脆弱帶來(lái) 時(shí)間: 2025-3-30 12:08 作者: 多節(jié) 時(shí)間: 2025-3-30 16:13
,Runge’s Theorem,If f ∈ .(G), G a connected open set, it is a consequence of the power series expansion for holomorphic functions that if f(z.) = 0, z. → z. ∈ G then f = 0 in G. It is also a consequence that if f.(z.) = 0 for n = 0,1,2,…, then f = 0 in G. We adopt conventions about “sets with multiplicity” that allow us to treat both cases as one.作者: LVAD360 時(shí)間: 2025-3-30 17:31 作者: Brittle 時(shí)間: 2025-3-30 23:02
The Riemann Mapping Theorem,The Riemann Mapping Theorem implies that, as far as . can tell, all simply connected regions are the “same”. To clarify what this means we need the following notion of equivalence.作者: Perineum 時(shí)間: 2025-3-31 01:11 作者: CURL 時(shí)間: 2025-3-31 08:05
Dual Space Topologies,This chapter is intended as a prerequisite for later chapters. In it we introduce a topology on the dual of a topological vector space. We present some of the standard results in the theory of Fréchet spaces and some additional results on topological vector spaces in general.作者: 宇宙你 時(shí)間: 2025-3-31 11:09
Universitexthttp://image.papertrans.cn/c/image/231343.jpg作者: 刪除 時(shí)間: 2025-3-31 13:42
Preliminaries: Set Theory and Topology,tion of a family of sets, set difference (AB), complement (compl A), Cartesian product; functions, domain, range, one-to-one, onto, image, inverse, restriction; partial ordering, linear (or total) ordering, and equivalence relation.作者: 過(guò)多 時(shí)間: 2025-3-31 18:27 作者: 整體 時(shí)間: 2025-3-31 23:33
,Duality of ,(G)—The Case of the Unit Disc,of seminorms. For each non-empty finite set A = {‖?‖., ‖?‖.,…, ‖?‖.} ? ., define., x ∈ E. Then ‖?‖. is a seminorm. Let . = . ∪ {‖?‖.: A is a non empty finite subset of .}; then . and . generate the same topology on E (Exercise 2). Consequently, we may assume . = . in the following proposition.作者: ALE 時(shí)間: 2025-4-1 04:45 作者: 清洗 時(shí)間: 2025-4-1 06:39 作者: 騷動(dòng) 時(shí)間: 2025-4-1 12:31
