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Krasnosel'skii M.A., Rtuickii Yz.B. — Convex Functions and Orlicz Spaces
Krasnosel'skii M.A., Rtuickii Yz.B. — Convex Functions and Orlicz Spaces

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Название: Convex Functions and Orlicz Spaces

Авторы: Krasnosel'skii M.A., Rtuickii Yz.B.

Аннотация:

In the present book are discussed the theory of extensive classes of convex functions which play an important role in many branches of mathematics. The theory of Orlicz spaces (i. e. normed spaces of which the LP spaces are a special case) is developed in detail and applications are pointed out.
The book is intended for mathematicians (students in upper level courses, aspirants for the doctoral degree and scientific workers), who deal with functional analysis and its applications and also with various problems in the theory of functions.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1961

Количество страниц: 259

Добавлена в каталог: 21.03.2013

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$E_{N}$-weakly continuous linear functionals      133
$\Delta'$-condition      29 219
$\Delta^{2}$-condition      40 220
$\Delta_{2}$—condition      23 218
$\Delta_{3}$-condition      35 220
Absolute continuity of the norm      87
Ahiezer      136 146 239
Albrycht      238 239
Amemiya      231 234 239
Banach      127 134 135 234 239
Banach’s theorem      134
Basis      101
Birnbaum      230 231 239
Branch      208
Branch, point      209 216
Calculation of the norm      88
Carath      6
Carath, conditions      167
Carath, odory      239
Characteristic values      208
Characteristic values, vectors      208
Class of completely continuous operators of continuous operators      137
Compact operator      194
Compactness criteria      94
Comparison of N-functions      14 218
Comparison of Orlicz classes      63
Comparison of spaces      110
Complementary N-function      11
Complete continuity of linear integral operators      149
Completely continuous operator      194
Completeness of Orlicz spaces      70
Composition of N-functions      10
Cone      213
Convex functions      1 217
Differentiability      176 181
Differentiable operator      179
Dinculeanu      232 238 239
Dubrovskii      237 240
Equivalence criterion      17
Equivalent N-functions      15
Fatou’s theorem      71
Fihtengol’c      189 240
Frechet derivative      179
Frechet derivative, differential      179
Frechet’s theorem      97
Gateaux gradient      186
Gateaux gradient, differentiable      186
Glazman      136 146 239
Golomb      236 237 240
Gradient of a functional      176
Gradient of the Luxemburg norm      187 225
Gradient of the norm      176
Gradient of the Orlicz norm      189
Gribanov      232 238 240
Haar      240
Haar, functions      103
Hammerstein      236 237 240
Hammerstein, operator      207
Hardy      230 240
Hille      128 236 240
Holder’s Inequality      72 223
Homogeneous function space      232
Inequality, Hoelder’s      72
Inequality, Jensen’s      1
Inequality, Young’s      13
Integral representation of a convex function      3
Jensen      230 240
Jensen’s Inequality      1
Kalugina      231 236 241
Kantorovic      231 235 236 237 241
Kipriyanov      231 241
Kolmogorov      241
Kolmogorov’s compactness criterion      97 225
Kondrasov      235
Korenblyum      231 241
Krasnosel’skii      167 170 202 212 213 215 230 231 232 233 234 235 236 237 238 241 242
Krein      235 236 237 242 243
Ladyzenski      167 236 237 242 243
Leray      237 243
Levi’s theorem      69
Linear functionals      124
Littlewood      230 240
Lozinski      230 231 243
Luxemburg      78 232 234 243
Luxemburg, gradient of      187
Luxemburg, norm      78 222
Luzin’s C-property      177
Lyusternik      131 236 243
Mean convergence      75
Medvedev      231 243
Milnes      238 243
Monotonic operator      213
Naimark      244
Nakano      231 232 244
Natanson      6 69 71 94 95 244
Nemyckii      212 236 237 243
Nonlinear integral equations      194
Nonlinear integral equations, operators      167
Norm, Luxemburg      78
Norm, Luxemburg of a functional      134
Norm, Luxemburg of the characteristic function      72
Operator, compact      194
Operator, completely continuous      194
Operator, Hammerstein      207
Operator, potential      214
Operator, Uryson      194
Operators in Orlicz spaces      137
Operators, completely continuous      137
Operators, continuous      137
Operators, differentiable      179
Operators, nonlinear      167
Orlicz      230 231 232 234 239 244
Orlicz, classes      60
Orlicz, gradient of      189
Orlicz, norm      67 221
Orlicz, operators in      137
Orlicz, space      69 221
Partially ordered set      15
Phillips      240
Pinsker      237 241s
Positive operator      213
Potential operator      214
Povolockii      236 242
Principal part of an N-function      16
Product of functions in Orlicz spaces      117
Properties of N-functions      7
Radon      234 244
Riesz      234 244
Riesz’s criterion for compactness      99 225
Rohlin      234 244
Rutickii      230 231 232 234 235 236 237 238 242 244
Rutman      237 243
Salehov      126 234 245
Schaffer      245
Schauder      237 243
Schauder’s principle      209
Scorza Dragoni      212 237 245
Separability of $E_{M}$      81
Set of complete measure      17
Silov      245
Silov’s theorem      233
Simko      232
Skvorcov      245
Sobolev      131 232 233 235 236 242 243 245
Solomyak      233 245
Space $E_{M}$      80
Space $E_{M}$, $L_{M}$      67
Space $E_{M}$, Orlicz      69
Spectrum      208
Splitting of a completely continuous operator      164
Splitting of a continuous operator      146
Sragin      238 246
Steklov functions      95
Sudakov      233
Sz. — Nagy      234 244
Szegoe      230 244
Takahashi      246
Tamarkin      233 246
Theorem on branch points      216
Theorem, Fatou’s      71
Theorem, Frechet’s      97
Theorem, Levi’s      69
Theorem, Silov’s      233
Theorem, Vallee Poussin’s      94
Theorem, Zaanen’s      155
Tulaikov      233 246
Uryson      246
Uryson, operator      194
Vainberg      186 236 237 246
Vallee Poussin’s theorem      94
Videnskii      238 246
Vulih      237 241
Weiss      238 246
Yamamuro      231 232 247
Young      247
Young’s inequality      13
Zaanen      235 243 247
Zaanen’s theorem      155
Zygmund      230 231 232 247
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