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Lang S. — Real and Functional Analysis (Graduate Texts in Mathematics Series #142)
Lang S. — Real and Functional Analysis (Graduate Texts in Mathematics Series #142)

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Название: Real and Functional Analysis (Graduate Texts in Mathematics Series #142)

Автор: Lang S.

Аннотация:

This book is meant as a text for a first-year graduate course in analysis. In a sense, the subject matter covers the same topics as elementary calculus - linear algebra, differentiation, integration - but treated in a manner suitable for people who will be using it in further mathematical investigations. The book begins with point-set topology, essential for all analysis. The second part deals with the two basic spaces of analysis, Banach and Hilbert spaces. The book then turns to the subject of integration and measure. After a general introduction, it covers duality and representation theorems, some applications (such as Dirac sequences and Fourier transforms), integration and measures on locally compact spaces, the Riemann-Stjeltes integral, distributions, and integration on locally compact groups. Part four deals with differential calculus (with values in a Banach space). The next part deals with functional analysis. It includes several major spectral theorems of analysis, showing how one can extend to infinite dimensions certain results from finite-dimensional linear algebra; a discussion of compact and Fredholm operators; and spectral theorems for Hermitian operators. The final part, on global analysis, provides an introduction to differentiable manifolds. The text includes worked examples and numerous exercises, which should be viewed as an integral part of the book. The organization of the book avoids long chains of logical interdependence, so that chapters are as independent as possible. This allows a course using the book to omit material from some chapters without compromising the exposition of material from later chapters.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: 3rd Edition

Год издания: 1993

Количество страниц: 580

Добавлена в каталог: 04.04.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Open covering      31
Open mapping theorem      388
Open set      17
Operator      66 73 105
Order of distribution      297
Ordering      10
Ordinary topology      18
Orientation      551
Oriented volume      499
Orthogonal      96 187
Orthogonal basis      98
Orthogonal decomposition      102
Orthogonal family      98
Orthogonal measures      192
Orthogonal projection      101 450
Orthonormal      98
Outer measure      154 259
Parallelogram      98 100
Parameters      370
Parseval formula      243
Partial derivatives      352
Partial isometry      454
Partition      122
Partition of unity      263 270 271 536
Peano curve      50
Perpendicular      96
Piecewise continuous      29
Poisson family      231
Poisson kernel      231
Poisson summation formula      244
Polar decomposition      454 460
Polarization      107
Positive definite      96 450
Positive functional      252 265
Positive measurable maps      173
Positive measure      119 446
Positive operator      441 446
Pre-Hilbert space      99
Product measure      160 177 214
Product measure on locally compact spaces      272
Product topology      26
Projection      101 450 166
Proper, map      48
Proper, subset      3
Pythagoras' theorem      98
Quadratic form      107
Radon — Nikodym derivative      218
Radon — Nikodym theorem      192 204
rectangle      158 167
Refinement of covering      536
Refinement of topology      23
Regular measure      256 265 267
Regular point      562
Regular space      48
Regularizing sequence      228
Regulated map      332
Relatively compact      35 415
Relatively invariant      323
Representation by a measure      191 195
Resolvant      412
Rieffel's theorem      208
Riemann — Lebesgue lemma      176 287 291
Riemann — Stieltjes integral      281
Riemann — Stieltjes measure      285
Riesz theorem      256 264 268
Schroedinger operator      233
Schur's lemma      452
Schwartz space      236
Schwarz inequality      96
Second derivative      344
Self adjoint      107 470
Semilinear      95
Seminorm      44
Semiparallelogram law      50
Separable      24 47
Separate closed sets      33
Separate points      33 52
Separation by continuous functions      40
SEQUENCE      4 7
Sequentially compact      33
Sesquilinear      95
Shrinking lemma      360
Shub's theorem      380
Simple map      118
Singular measure      192
Singular point      562
Size of partition      278
Skew symmetric      460
Spectral family      466 490 493
Spectral integral      492
Spectral measure      481
Spectral radius      406
Spectral theorems, bounded hermitian operators      447
Spectral theorems, compact operators      426 431 443
Spectral theorems, self-adjoint operators      470
Spectrum      400 442 446
Sphere      20
Square root of operator      446
Step map      122 148 184 331
Stieltjes integral      281 491
Stokes' theorem      555 558
Stokes' theorem with singularities      563
Stone — Weierstrass theorem      52 61 62 273 446
Strictly inductively ordered      12
Strong convergence      435
Subcovering      31
Submanifold      528
Subordinated      271 536
Subsequence      8
subspace      22
Summation by parts      282
Sup norm      18
Support      255 299 550
Surjective      3
Surjective mapping theorem      397
symmetric      438 470
Tangent bundle      535
Tangent map      534
Tangent space      533
Tangent vector      533
Taylor's formula      349
Theta function      248
Tietze extension theorem      42
Time-dependent vector field      369
Titchmarsh — Kodaira formula      487
Toplinear isomorphism      67
Topological group      308
Topological isomorphism      25
Topological space      21
topology      17
Tornheim's proof      401
Total family      98
Total ordering      11
Total variation      197
Totally bounded      35
Totally ordered      11
Trace      436 462
Trace, class      462
Transition map      525
Translation      170 309
TRANSPOSE      106
Trivializing chart      536
Tychonoff's theorem      37
uniform      19
Uniform, boundedness      395
Uniform, convergence      19
Uniform, convergence on compact sets      46
Uniformly continuous      36 309
UNIT      71 413
Unit vector      97
Unitary      439
Unitary, group      325 328
Upper bound      11
Urysohn's lemma      40 45
Urysohn's metrization theorem      48
Value      3
Variation      278
Variation, function      279
Vector field      365 544
Vectorial measure      199
Weak convergence      107
Weak topology      24 71
Weakly measurable      174
Weierstrass approximation      229
Weierstrass — Bolzano property      33
Zariski topology      22
Zero      21
Zero of ideal      56
Zorn's lemma      12 16
1 2
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