Atjaunināt sīkdatņu piekrišanu

E-grāmata: Introduction to Modern Analysis

(Professor Emeritus of Mathematics, Bar-Ilan University), (Senior Lecturer, University of Haifa)
Citas grāmatas par šo tēmu:
  • Formāts - PDF+DRM
  • Cena: 46,38 €*
  • * ši ir gala cena, t.i., netiek piemērotas nekādas papildus atlaides
  • Ielikt grozā
  • Pievienot vēlmju sarakstam
  • Šī e-grāmata paredzēta tikai personīgai lietošanai. E-grāmatas nav iespējams atgriezt un nauda par iegādātajām e-grāmatām netiek atmaksāta.
Introduction to Modern AnalysisPalielināt
Citas grāmatas par šo tēmu:

DRM restrictions

  • Kopēšana (kopēt/ievietot):

    nav atļauts

  • Drukāšana:

    nav atļauts

  • Lietošana:

    Digitālo tiesību pārvaldība (Digital Rights Management (DRM))
    Izdevējs ir piegādājis šo grāmatu šifrētā veidā, kas nozīmē, ka jums ir jāinstalē bezmaksas programmatūra, lai to atbloķētu un lasītu. Lai lasītu šo e-grāmatu, jums ir jāizveido Adobe ID. Vairāk informācijas šeit. E-grāmatu var lasīt un lejupielādēt līdz 6 ierīcēm (vienam lietotājam ar vienu un to pašu Adobe ID).

    Nepieciešamā programmatūra
    Lai lasītu šo e-grāmatu mobilajā ierīcē (tālrunī vai planšetdatorā), jums būs jāinstalē šī bezmaksas lietotne: PocketBook Reader (iOS / Android)

    Lai lejupielādētu un lasītu šo e-grāmatu datorā vai Mac datorā, jums ir nepieciešamid Adobe Digital Editions (šī ir bezmaksas lietotne, kas īpaši izstrādāta e-grāmatām. Tā nav tas pats, kas Adobe Reader, kas, iespējams, jau ir jūsu datorā.)

    Jūs nevarat lasīt šo e-grāmatu, izmantojot Amazon Kindle.

This textbook provides an introduction to modern analysis aimed at advanced undergraduate and graduate-level students of mathematics. Professional academics will also find this to be a useful reference work. It covers measure theory, basic functional analysis, single operator theory, spectral theory of bounded and unbounded operators, semigroups of operators, and Banach algebras. Further, this new edition of the textbook also delves deeper into C*-algebras and their standard constructions, von Neumann algebras, probability and mathematical statistics, and partial differential equations.

Most chapters contain relatively advanced topics alongside simpler ones, starting from the very basics of modern analysis and slowly advancing to more involved topics. The text is supplemented by many exercises, to allow readers to test their understanding and practical analysis skills.

Recenzijas

Most chapters contain relatively advanced topics alongside simpler ones, starting from the very basics of modern analysis and slowly advancing to more involved topics. The text is supplemented by many exercises, to allow readers to test their understanding and practical analysis skills. * MathSciNet * There are plenty of exercises in each chapter to reinforce the readers' comprehension of the topics being covered, a good bibliography, and an excellent index which occupies 14 pages. Professional academics will also find this to be a very useful reference work. * Peter Shiu, The Mathematical Gazette *

Preface to the First Edition xv
Preface to the Second Edition xvii
1 Measures
1(58)
1.1 Measurable sets and functions
2(6)
1.2 Positive measures
8(2)
1.3 Integration of non-negative measurable functions
10(6)
1.4 Integrable functions
16(7)
1.5 Lp-spaces
23(7)
1.6 Inner product
30(3)
1.7 Hilbert space: a first look
33(2)
1.8 The Lebesgue--Radon--Nikodym theorem
35(5)
1.9 Complex measures
40(7)
1.10 Convergence
47(3)
1.11 Convergence on finite measure space
50(1)
1.12 Distribution function
51(2)
1.13 Truncation
53(6)
Exercises
55(4)
2 Construction of measures
59(22)
2.1 Semi-algebras
59(3)
2.2 Outer measures
62(2)
2.3 Extension of measures on algebras
64(1)
2.4 Structure of measurable sets
65(2)
2.5 Construction of Lebesgue--Stieltjes measures
67(3)
2.6 Riemann vs. Lebesgue
70(1)
2.7 Product measure
71(10)
Exercises
76(5)
3 Measure and topology
81(26)
3.1 Partition of unity
81(3)
3.2 Positive linear functionals
84(7)
3.3 The Riesz--Markov representation theorem
91(2)
3.4 Lusin's theorem
93(4)
3.5 The support of a measure
97(1)
3.6 Measures on Rk; differentiability
97(10)
Exercises
101(6)
4 Continuous linear functionals
107(22)
4.1 Linear maps
108(2)
4.2 The conjugates of Lebesgue spaces
110(4)
4.3 The conjugate of Cc(X)
114(2)
4.4 The Riesz representation theorem
116(2)
4.5 Haar measure
118(11)
Exercises
126(3)
5 Duality
129(44)
5.1 The Hahn--Banach theorem
130(4)
5.2 Reflexivity
134(3)
5.3 Separation
137(3)
5.4 Topological vector spaces
140(3)
5.5 Weak topologies
143(3)
5.6 Extremal points
146(4)
5.7 The Stone--Weierstrass theorem
150(2)
5.8 Operators between Lebesgue spaces: Marcinkiewicz's interpolation theorem
152(5)
5.9 Fixed points
157(8)
5.10 The bounded weak-topology
165(8)
Exercises
169(4)
6 Bounded operators
173(20)
6.1 Category
174(1)
6.2 The uniform boundedness theorem
175(2)
6.3 The open mapping theorem
177(2)
6.4 Graphs
179(2)
6.5 Quotient space
181(1)
6.6 Operator topologies
182(11)
Exercises
184(9)
7 Banach algebras
193(32)
7.1 Basics
194(9)
7.2 Commutative Banach algebras
203(4)
7.3 Involutions and C*-algebras
207(4)
7.4 Normal elements
211(1)
7.5 The Arens products
212(13)
Exercises
215(10)
8 Hilbert spaces
225(28)
8.1 Orthonormal sets
225(3)
8.2 Projections
228(3)
8.3 Orthonormal bases
231(3)
8.4 Hilbert dimension
234(1)
8.5 Isomorphism of Hilbert spaces
235(1)
8.6 Direct sums
236(1)
8.7 Canonical model
237(1)
8.8 Tensor products
237(16)
8.8.1 An interlude: tensor products of vector spaces
237(3)
8.8.2 Tensor products of Hilbert spaces
240(2)
Exercises
242(11)
9 Integral representation
253(36)
9.1 Spectral measure on a Banach subspace
254(1)
9.2 Integration
255(2)
9.3 Case Z = X
257(3)
9.4 The spectral theorem for normal operators
260(2)
9.5 Parts of the spectrum
262(2)
9.6 Spectral representation
264(1)
9.7 Renorming method
265(2)
9.8 Semi-simplicity space
267(3)
9.9 Resolution of the identity on Z
270(4)
9.10 Analytic operational calculus
274(3)
9.11 Isolated points of the spectrum
277(2)
9.12 Compact operators
279(10)
Exercises
282(7)
10 Unbounded operators
289(34)
10.1 Basics
290(3)
10.2 The Hilbert adjoint
293(3)
10.3 The spectral theorem for unbounded selfadjoint operators
296(2)
10.4 The operational calculus for unbounded selfadjoint operators
298(2)
10.5 The semi-simplicity space for unbounded operators in Banach space
300(3)
10.6 Symmetric operators in Hilbert space
303(4)
10.7 Quadratic forms
307(16)
Exercises
311(12)
11 C*-algebras
323(32)
11.1 Notation and examples
324(1)
11.2 The continuous operational calculus continued
325(2)
11.3 Positive elements
327(5)
11.4 Approximate identities
332(1)
11.5 Ideals
333(2)
11.6 Positive linear functionals
335(5)
11.7 Representations and the Gelfand--Naimark--Segal construction
340(6)
11.7.1 Irreducible representations
345(1)
11.8 Positive linear functionals and convexity
346(9)
11.8.1 Pure states
346(3)
11.8.2 Decompositions of functionals
349(1)
Exercises
350(5)
12 Von Neumann algebras
355(28)
12.1 Preliminaries
356(3)
12.2 Commutants
359(3)
12.3 Density
362(1)
12.4 The polar decomposition
363(2)
12.5 W*-algebras
365(3)
12.6 Hilbert--Schmidt and trace-class operators
368(7)
12.7 Commutative von Neumann algebras
375(1)
12.8 The enveloping von Neumann algebra of a C*-algebra
376(7)
Exercises
379(4)
13 Constructions of C*-algebras
383(26)
13.1 Tensor products of C*-algebras
383(14)
13.1.1 Tensor products of algebras
384(1)
13.1.2 Tensor products of C*-algebras through representations
385(5)
13.1.3 The maximal tensor product
390(1)
13.1.4 Tensor products of bounded linear functionals
390(3)
13.1.5 The minimal tensor product
393(3)
13.1.6 Tensor products by commutative C*-algebras
396(1)
13.2 Group C*-algebras
397(12)
13.2.1 Unitary representations
398(2)
13.2.2 The definition and representations of the group C*-algebra
400(1)
13.2.3 Properties of the group C*-algebra
401(2)
Exercises
403(6)
Application I Probability
409(82)
I.1 Heuristics
409(2)
I.2 Probability space
411(13)
I.2.1 L2-random variables
414(10)
I.3 Probability distributions
424(9)
I.4 Characteristic functions
433(8)
I.5 Vector-valued random variables
441(9)
I.6 Estimation and decision
450(12)
I.6.1 Confidence intervals
455(2)
I.6.2 Testing of hypothesis and decision
457(3)
I.6.3 Tests based on a statistic
460(2)
I.7 Conditional probability
462(13)
I.7.1 Heuristics
462(5)
I.7.2 Conditioning by an r.v.
467(8)
I.8 Series of L2 random variables
475(6)
I.9 Infinite divisibility
481(4)
I.10 More on sequences of random variables
485(6)
Application II Distributions
491(58)
II.1 Preliminaries
491(2)
II.2 Distributions
493(10)
II.3 Temperate distributions
503(17)
II.3.1 The spaces Wp,k
514(6)
II.4 Fundamental solutions
520(3)
II.5 Solution in ε'
523(2)
II.6 Regularity of solutions
525(3)
II.7 Variable coefficients
528(3)
II.8 Convolution operators
531(11)
II.9 Some holomorphic semigroups
542(7)
Bibliography 549(4)
Index 553
Shmuel Kantorovitz received his Ph.D. from the University of Minnesota in 1962. After postdocs at Princeton University and the Institute for Advanced Study in Princeton, he took on an Assistant Professorship at Yale University, and became an Associate and then Full Professor at the University of Illinois in Chicago. He then returned to Israel to become a Full Professor at Bar-Ilan University, where he is now Professor Emeritus.



Ami Viselter received his Ph.D. from Bar-Ilan University in 2009. After postdocs in the Technion - Israel Institute of Technology and at the University of Alberta, he became a faculty member at the University of Haifa, where he is currently a tenured Senior Lecturer.
Biežāk uzdotie jautājumi par e-grāmatām Biežāk uzdotie jautājumi par e-grāmatām
Permanent link: https://www.kriso.lv/db/97801926661922e.html
Keywords: