D'Angelo J.P. — Inequalities from Complex Analysis (Carus Mathematical Monographs) :: Электронная библиотека попечительского совета мехмата МГУ

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D'Angelo J.P. — Inequalities from Complex Analysis (Carus Mathematical Monographs)

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Название: Inequalities from Complex Analysis (Carus Mathematical Monographs)

Автор: D'Angelo J.P.

Аннотация:

Inequalities from Complex Analysis is a careful, friendly exposition of some rather interesting mathematics. The author begins by defining the complex number field; he gives a novel presentation of some standard mathematical analysis in the early chapters. The development culminates with some results from recent research literature. The book provides complete yet comprehensible proofs as well as some surprising consequences of the results. One unifying theme is a complex variables analogue of Hilbert's seventeenth problem. Numerous examples, exercises and discussions of geometric reasoning aid the reader. The book is accessible to undergraduate mathematicians, as well as physicists and engineers.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель без номеров страниц

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Год издания: 2002

Количество страниц: 277

Добавлена в каталог: 01.07.2020

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Предметный указатель

8—commutator      169 240
Abelian group      248
Absolute value      5
Adjoint      90
anti-holomorphic      79
Arithmetic-geometric mean inequality      180 196
Artin, E.      179 245
Arzel $\grave a$ — Ascoli theorem      165 254
Automorphism      6 85
Banach space      40 102 129 143 252
Bergman kernel function      63 78—87 94 237 244
Bergman projection      94—95 238
beta function      63 73 75 171 173
bihomogeneous      181 188 191—192 217—222
Blaschke product      230
Bochner's theorem      89 129 138
bordered complex Hessian      204 244
Bounded linear transformation      43 90 93 98 144
Catlin, D.      218 222
Cauchy integral formula      22
Cauchy principal value      168—169
Cauchy sequence      2 16 43 252
Cauchy — Schwarz inequality      36 49 50 81 82 84 127 128 140 147 156 157 163 167 244
Ces $\grave a$ ro means      24 129 131 132 135 141
circle      9
Closed disk      9
Compact operator      89 143—166 236 238 243 244
Compactification      228
Complete metric space      3 16 145 252
Complete ordered field      1 250
Complete orthonormal system      51 72 75 80
Completeness axiom      2
Complex analytic      22
Complex conjugation      5
Complex Euclidean space      33—61 89
complex Hessian      198 200 204
Complex number field      3—8
Complex projective space      43 244
conjugate holomorphic      79
Convergence in norm      144
Convex      197
Convex combination      123
Convexity inequality      197
Cosine      25
Curve      194—195
Cyclic group      30
de Moivre's formula      26 28
Diagonal      182
Differentiable      101
Dirac delta function      132
Dirac measure      130 132 134
Distance      15 145 251
Distribution theory      199
Domain      65
Eigenspace      154 158
Eigenvalue      89 105—109 110 154 155 158
Eigenvector      105 155 158
Equicontinuous      164 254—255
Euclidean distance      8
Euclidean inner product      9 34
Euclidean norm      34
Euler's formula      206
Exponential      25
Exponential generating function      57 59
Fej $\acute e$ r's theorem      89 129 132 134 170
Field      2 248
Finite type      84
Fourier integral operator      173
Fourier inversion formula      172 174
Fourier series      89 124 125
Fourier transform      137 171—172 173
Fredholm alternative      99
Fundamental theorem of algebra      230 243
Gamma function      63 73 77
Gegenbauer polynomials      61
Generating function      56—57 86
Geometric series      19 22 57 83 133
global Cauchy — Schwarz inequality      209—210 213
Gram — Schmidt process      55
Group      247
Hadamard inequalities      120—121
Hankel matrix      124 127 128
Harmonic      68
Hartogs, F.      66
Herglotz's theorem      89 129 136
Hermite polynomials      59 60
Hermitian      91 93 168
Hermitian form      90 92 175
Hermitian inner product      33 35
Hermitian inner product, continuity of      38
Hermitian linear transformation      89 106 110
hessian      198 200
Hilbert space      40 33—61 70 89 102 143
Hilbert transform      168
Hilbert's inequality      124—128
Hilbert's seventeenth problem      179 245
holomorphic decomposition      184
Holomorphic function      22 65 63—69 102 122
Homogeneous      64 77 196
Hyperplane      50
Ideal      14 151
Imaginary part      4 69
Integral operator      143 152 160 162—174 237
isometric imbedding theorem      243
Isometry      6 97 132
jet pullback property      195—196 222
Kodaira imbedding theorem      244

Lagrange multipliers      104 107 180
Laguerre polynomials      57
Law of Cosines      39
Least squares      99—101 103
Legendre polynomials      60
lim inf, lim sup      16
Linear fractional transformation      85
Linear functional      44 71
Linear subspace      42
Linearization      101—105
logarithmically plurisubharmonic      200 205—207
Mathematica      182 213
Matrix of coefficients      183 187 190—192 208
Maximal ideal      14
Mean-value property      68
Measure      130
Metric space      15 251
Minkowski inequality      123
Multi-index notation      63 64 72—73
Nonnegative definite      91 119
Norm      35 36
norm, continuity of      38
Normed linear space      251
NullSpace      97
Nullstellensatz      243
Objective function      104
Open disk      9
Open unit ball      39 72 83—86 227—231
Operator      89
Ordered field      2 248 250
Ordinary generating function      57
Orthogonal      9 45 154
Orthogonal sum      185
Orthonormal expansion      52
Orthonormal system      51 57 58 72 75 80
P $\acute o$ lya's theorem      176 181 220 221
Parallelogram law      11
Parseval's formula      131
Partial sum      19 82 131 141
Perpendicular      9
Plancherel theorem      172
Plurisubharmonic      197—207
Poincar $\acute e$ inequalities      140
Point spectrum      105
Poisson integral      235
Poisson kernel      71
Polar representation      27
Polarization      28 30 156
Polarization identity      41 53—55
Positive definite      35 89 91 110—123 153 190
Positive type      129 138
positivity conditions      89 175—215 220 225—227 231—233
Power series      19
Primitive root of unity      30
principal minor determinant      114 116 119 123
Projection      46 78 91 94 169 186
Proper holomorphic mapping      227—231
Pseudoconvex      84
Pseudodifferential operator      173
Pythagorean Theorem      39 45 48
Quillen, D.      218
quotient of squared norms      193—196 223—225
Quotient ring      14
Radius of convergence      21
RANGE      97 152
Ratio Test      21
Real part      4 69
Reciprocal      7
Region of convergence      21 67
Reproducing property      79
Riesz representation      49 70 78 90 129
Rodrigues formula      58
Root of unity      30—32
Schroedinger equation      59
Schur product      121
Schwartz, L.      172
Self-adjoint      91
Separable      51
Sesquilinear form      35 92
Sine      25
Singular integral operator      166
small-constant large-constant trick      147
Smoothing operator      99
Spectral theorem      89 105 143 153—159 190
Spectrum      105
Squared norm      193—196 217
Stabilization      217—222 233—241
Strong operator topology      144 153
Subharmonic      198 201—202
Tensor product      121 185—186
Toeplitz matrix      124 128
Triangle inequality      15 36
Trichotomy      2
Trigonometric polynomial      124 135 169 170
Trigonometric series      124
Ultraspherical polynomials      61
Unbounded operator      45
Uniform convergence      40 77 165 179
Unitary      91 95 168 172 186
Universal line bundle      243 244
Vector space      34 249
Vector-valued      67
Veronese mapping      189
Volterra integral operator      160
Weak derivative      199
Weak operator topology      144
Weierstrass approximation theorem      109 129 142
Wirtinger's inequality      89 139—140 161

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