Muutke küpsiste eelistusi

E-raamat: Metric Embeddings: Bilipschitz and Coarse Embeddings into Banach Spaces

4.00/5 (2 hinnangut Goodreads-ist)
Teised raamatud teemal:
  • Formaat - PDF+DRM
  • Hind: 182,32 €*
  • * hind on lõplik, st. muud allahindlused enam ei rakendu
  • Lisa ostukorvi
  • Lisa soovinimekirja
  • See e-raamat on mõeldud ainult isiklikuks kasutamiseks. E-raamatuid ei saa tagastada.
  • Raamatukogudele
    • De Gruyter e-raamatud
Metric Embeddings: Bilipschitz and Coarse Embeddings into Banach SpacesSuurem pilt
Teised raamatud teemal:

DRM piirangud

  • Kopeerimine (copy/paste):

    ei ole lubatud

  • Printimine:

    ei ole lubatud

  • Kasutamine:

    Digitaalõiguste kaitse (DRM)
    Kirjastus on väljastanud selle e-raamatu krüpteeritud kujul, mis tähendab, et selle lugemiseks peate installeerima spetsiaalse tarkvara. Samuti peate looma endale  Adobe ID Rohkem infot siin. E-raamatut saab lugeda 1 kasutaja ning alla laadida kuni 6'de seadmesse (kõik autoriseeritud sama Adobe ID-ga).

    Vajalik tarkvara
    Mobiilsetes seadmetes (telefon või tahvelarvuti) lugemiseks peate installeerima selle tasuta rakenduse: PocketBook Reader (iOS / Android)

    PC või Mac seadmes lugemiseks peate installima Adobe Digital Editionsi (Seeon tasuta rakendus spetsiaalselt e-raamatute lugemiseks. Seda ei tohi segamini ajada Adober Reader'iga, mis tõenäoliselt on juba teie arvutisse installeeritud )

    Seda e-raamatut ei saa lugeda Amazon Kindle's. 

Embeddings of discrete metric spaces into Banach spaces recently became an important tool in computer science and topology. The book will help readers to enter and to work in this very rapidly developing area having many important connections with different parts of mathematics and computer science. The purpose of the book is to present some of the most important techniques and results, mostly on bilipschitz and coarse embeddings. The topics include embeddability of locally finite metric spaces into Banach spaces is finitely determined, constructions of embeddings, distortion in terms of Poincar? inequalities, constructions of families of expanders and of families of graphs with unbounded girth and lower bounds on average degrees, Banach spaces which do not admit coarse embeddings of expanders, structure of metric spaces which are not coarsely embeddable into a Hilbert space, applications of Markov chains to embeddability problem, metric characterizations of properties of Banach spaces, and Lipschitz free spaces.

Mikhail I. Ostrovskii, St. John's University, Queens, USA.
Preface v
1 Introduction: examples of metrics, embeddings, and applications
1(33)
1.1 Metric spaces: definitions and main examples
1(5)
1.2 Types of embeddings: isometric, bilipschitz, coarse, and uniform
6(16)
1.2.1 Isometric embeddings
6(3)
1.2.2 Bilipschitz embeddings
9(8)
1.2.3 Coarse and uniform embeddings
17(5)
1.3 Probability theory terminology and notation
22(3)
1.4 Applications to the sparsest cut problem
25(1)
1.5 Exercises
26(1)
1.6 Notes and remarks
27(3)
1.6.1 To Section 1.1
27(1)
1.6.2 To Section 1.2
28(1)
1.6.3 To Section 1.3
29(1)
1.6.4 To Section 1.4
30(1)
1.6.5 To exercises
30(1)
1.7 On applications in topology
30(2)
1.8 Hints to exercises
32(2)
2 Embeddability of locally finite metric spaces into Banach spaces is finitely determined. Related Banach space theory
34(46)
2.1 Introduction
34(1)
2.2 Banach space theory: ultrafilters, ultraproducts, finite representability
35(9)
2.2.1 Ultrafilters
35(2)
2.2.2 Ultraproducts
37(3)
2.2.3 Finite representability
40(4)
2.3 Proofs of the main results on relations between embeddability of a locally finite metric space and its finite subsets
44(9)
2.3.1 Proof in the bilipschitz case
44(8)
2.3.2 Proof in the coarse case
52(1)
2.3.3 Remarks on extensions of finite determination results
53(1)
2.4 Banach space theory: type and cotype of Banach spaces, Khinchin and Kahane inequalities
53(22)
2.4.1 Rademacher type and cotype
53(4)
2.4.2 Kahane-Khinchin inequality
57(9)
2.4.3 Characterization of spaces with trivial type or cotype
66(9)
2.5 Some corollaries of the theorems on finite determination of embeddability of locally finite metric spaces
75(1)
2.6 Exercises
76(1)
2.7 Notes and remarks
77(2)
2.8 Hints to exercises
79(1)
3 Constructions of embeddings
80(25)
3.1 Padded decompositions and their applications to constructions of embeddings
80(4)
3.2 Padded decompositions of minor-excluded graphs
84(6)
3.3 Padded decompositions in terms of ball growth
90(3)
3.4 Gluing single-scale embeddings
93(9)
3.5 Exercises
102(1)
3.6 Notes and remarks
102(2)
3.7 Hints to exercises
104(1)
4 Obstacles for embeddability: Poincare inequalities
105(26)
4.1 Definition of Poincare inequalities for metric spaces
105(2)
4.2 Poincare inequalities for expanders
107(5)
4.3 Lp-distortion in terms of constants in Poincare inequalities
112(2)
4.4 Euclidean distortion and positive semidefinite matrices
114(2)
4.5 Fourier analytic method of getting Poincare inequalities
116(11)
4.6 Exercises
127(1)
4.7 Notes and remarks
128(1)
4.8 A bit of history of coarse embeddability
129(1)
4.9 Hints to exercises
130(1)
5 Families of expanders and of graphs with large girth
131(60)
5.1 Introduction
131(1)
5.2 Spectral characterization of expanders
132(5)
5.3 Kazhdan's property (T) and expanders
137(5)
5.4 Groups with property (T)
142(4)
5.4.1 Finite generation of SLn(Z)
143(1)
5.4.2 Finite quotients of SLn(Z)
144(1)
5.4.3 Property (T) for groups SLn(Z)
145(1)
5.4.4 Criterion for property (T)
145(1)
5.5 Zigzag products
146(9)
5.6 Graphs with large girth: basic definitions
155(1)
5.7 Graph lift constructions and embeddable graphs with large girth
156(8)
5.8 Probabilistic proof of existence of expanders
164(3)
5.9 Size and diameter of graphs with large girth: basic facts
167(2)
5.10 Random constructions of graphs with large girth
169(1)
5.11 Graphs with large girth using variational techniques
170(4)
5.12 Inequalities for the spectral gap of graphs with large girth
174(1)
5.13 Biggs's construction of graphs with large girth
175(2)
5.14 Margulis's 1982 construction of graphs with large girth
177(1)
5.15 Families of expanders which are not coarsely embeddable one into another
178(3)
5.16 Exercises
181(2)
5.17 Notes and remarks
183(6)
5.17.1 Bounds for spectral gaps
187(1)
5.17.2 Graphs with very large spectral gaps
187(1)
5.17.3 Some more results and constructions
188(1)
5.18 Hints to exercises
189(2)
6 Banach spaces which do not admit uniformly coarse embeddings of expanders
191(27)
6.1 Banach spaces whose balls admit uniform embeddings into L1
192(3)
6.2 Banach spaces not admitting coarse embeddings of expander families, using interpolation
195(5)
6.3 Banach space theory: a characterization of reflexivity
200(4)
6.4 Some classes of spaces whose balls are not uniformly embeddable intoL1
204(4)
6.4.1 Stable metric spaces and iterated limits
204(2)
6.4.2 Non-embeddability result
206(2)
6.5 Examples of non-reflexive spaces with nontrivial type
208(7)
6.6 Exercises
215(1)
6.7 Notes and remarks
215(2)
6.8 Hints to exercises
217(1)
7 Structure properties of spaces which are not coarsely embeddable into a Hilbert space
218(10)
7.1 Expander-like structures implying coarse non-embeddability into L1
218(2)
7.2 On the structure of locally finite spaces which do not admit coarse embeddings into a Hilbert space
220(3)
7.3 Expansion properties of metric spaces not admitting a coarse embedding into a Hilbert space
223(3)
7.4 Exercises
226(1)
7.5 Notes and remarks
226(1)
7.6 Hints to exercises
227(1)
8 Applications of Markov chains to embeddability problems
228(37)
8.1 Basic definitions and results on finite Markov chains
228(2)
8.2 Markov type
230(2)
8.3 First application of Markov type to embeddability problems: Euclidean distortion of graphs with large girth
232(1)
8.4 Banach space theory: renormings of superreflexive spaces, q-convexity and p-smoothness
233(20)
8.4.1 Definitions and duality
233(6)
8.4.2 Pisier theorem on renormings of uniformly convex spaces
239(14)
8.5 Markov type of uniformly smooth Banach spaces
253(6)
8.6 Applications of Markov type to lower estimates of distortions of embeddings into uniformly smooth Banach spaces
259(2)
8.7 Exercises
261(1)
8.8 Notes and remarks
262(2)
8.9 Hints to exercises
264(1)
9 Metric characterizations of classes of Banach spaces
265(43)
9.1 Introduction
265(1)
9.2 Proof of the Ribe theorem through Bourgain's discretization theorem
266(21)
9.2.1 Proving Bourgain's discretization theorem. Preliminary step: it suffices to consider spaces with differentiable norm
268(1)
9.2.2 First step: picking the system of coordinates
269(2)
9.2.3 Second step: construction of a Lipschitz almost-extension
271(5)
9.2.4 Third step: further smoothing of the map using Poisson kernels
276(7)
9.2.5 Poisson kernel estimates and proofs of Lemmas 9.14 and 9.15
283(4)
9.3 Test-space characterizations
287(15)
9.3.1 More Banach space theory: superreflexivity
289(8)
9.3.2 Characterization of superreflexivity in terms of diamond graphs
297(5)
9.4 Exercises
302(1)
9.5 Notes and remarks
303(4)
9.5.1 Another test-space characterization of superreflexivity: binary trees
305(1)
9.5.2 Further results on test-spaces
306(1)
9.5.3 Further results on the Ribe program
307(1)
9.5.4 Non-local properties
307(1)
9.6 Hints to exercises
307(1)
10 Lipschitz free spaces
308(20)
10.1 Introductory remarks
308(1)
10.2 Lipschitz free spaces: definition and properties
308(4)
10.3 The case where dx is a graph distance
312(5)
10.4 Lipschitz free spaces of some finite metric spaces
317(9)
10.5 Exercises
326(1)
10.6 Notes and remarks
326(1)
10.7 Hints to exercises
327(1)
11 Open problems
328(7)
11.1 Embeddability of expanders into Banach spaces
328(2)
11.2 Obstacles for coarse embeddability of spaces with bounded geometry into a Hilbert space
330(2)
11.2.1 The main problem
330(1)
11.2.2 Comments
331(1)
11.3 Embeddability of graphs with large girth
332(1)
11.4 Coarse embeddability of a Hilbert space into Banach spaces
333(2)
Bibliography 335(26)
Author index 361(6)
Subject index 367
Mikhail I. Ostrovskii, St. John's University, Queens, USA.
Lisainfo e-raamatute kohta Lisainfo e-raamatute kohta
Püsilink: https://www.kriso.ee/db/97831102640122e.html
Märksõnad: