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Aczel J., Dhombres J. — Functional equations in several variables with applications to mathematics, information theory and to the natural and social sciences
Aczel J., Dhombres J. — Functional equations in several variables with applications to mathematics, information theory and to the natural and social sciences

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Название: Functional equations in several variables with applications to mathematics, information theory and to the natural and social sciences

Авторы: Aczel J., Dhombres J.

Аннотация:

Deals with modern theory of functional equations in several variables and their applications to mathematics, information theory, and the natural, behavioral, and social sciences. The authors emphasize applications, although not at the expense of theory, and have kept the prerequisites to a minimum; the reader should be familiar with calculus and some simple structures of algebra and have a basic knowledge of Lebesque integration. For the applications the authors have included references and explained the results used. The book is designed so that the chapters may be read almost independently of each other, enabling a selection of material to be chosen for introductory and advanced courses. Each chapter concludes with exercises and further results, 400 in all, which extend and test the material presented in the text. The history of functional equations is well documented in a final chapter which is complemented by an encyclopedic bibliography of over 1600 items. This volume will be of interest to professionals and graduate students in pure and applied mathematics.
This treatise deals with modern theory of functional equations in several variables and their applications to mathematics, information theory, and the natural, behavioural and social sciences. The authors have chosen to emphasize applications, though not at the expense of theory, so they have kept the prerequisites to a minimum.


Язык: en

Рубрика: Математика/

Серия: Сделано в холле

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1989

Количество страниц: 475

Добавлена в каталог: 15.05.2011

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
A-average      269
Abel's equation      377
Addition theorem (-formulae)      209
Additive extension      20 85 89 100 124 276
Additive function      2 20 4 46 78 83 85 86 88 91 99 101 121 122 124 6 128 139 42 163 165 167 168 186 191 238 241 262 4 270 275 8 281 282 284 286
Additive number theoretical function      265 277
Additively A-expandable      85
Additively expandable      85 87 88 101 284
Addundant      85 254 256 257 263 283 284
Admissible function      8 105 346
Af-affine functions      251
Affine space      74 120
Affine transformation      144
Afline geometry      74 75
Alaoglu — Bourbaki theorem      149
Algebraic number over a field      58
Alignment chart      300 302
allocation      99 100
Almost everywhere      93 94 111 155 236 340
Almost periodic Bohr function      66 71 93 148 151 4 162 163
Anamorphosis      300
Angels      20
Angle of parallelism      108
Angles (of two vectors)      2 105 106
Antiendomorphism      83
Antihomomorphism      83
Arithmetic mean      240 249 357 376
Associativity equation, conditional      297
Associativity equation, generalized      308
Astronomy      377
Asymptotic relation      31
Automata      377
Automorphism      57 59 70 78
Average returns      351
Averaging operator      331 333 334 336
Averaging set      336
Axiom of Choice      371
Baire property      263 286
Banach algebra      93 149 153 155 225 331 338 339
Banach space      47 92 129 130 155 376
Banach — Stone Theorem      147
Baxter operator      334 343 344
Bell polynomials      202 207
Bernoulli polynomial      344
Bernstein representation theorem      138
Biadditive function      66 167 170 194
Bicomplex plane      78
Bilinear form      195
Binomial theorem, series      31 365 367
Binomial type polynomials      202 205
Bisymmetry (mediality)      8 107 287 293 5 298
Bit      269 270
Bochner's theorem      110 155
Bohr group      60 65 98 149 151 153 5 161 162
Borel set      128
Bounded linear operator      37 47 50 130 134 335 337 339
Bounded solution of a functional equation      15 18 26 27 29 30 32 35 37 90 91 108 109 112 120 127 136 202 205 206 346 371
Buffer of capacity      269
C-addundant      86 191
Cancellative      22
Cancellativity      22 296 297 342
Cantor set      21 24
Capital      346 347
Cartesian square      11 213 214 217 222
Casorati determinant      230
Cauchy — Schwarz inequality      110 112 131
Cauchy’s equation      1 4 12 18 22 23 25 29 30 34 35 37 42 52 54 56 57 65 69 73 75 79 82 87 88 90 2 99 105 113 121 127 139 144 203 204 206 241 248 265 273 274 298 311 338 364 366 368 370 3 375 377
Cauchy’s equations, conditional      73 75 79 82 84 85 88 92 93 99 100 114 155 186 254 262 266 283 373
Cauchy’s exponential equation      28 31 3 38 47 54 93 138 206 209 225 273 311 366 373
Cauchy’s logarithmic equation      25 27 372
Cauchy’s power equation      29 32 40 47 376
CHARACTER      65 71 108 109 111 112 148 51 155 163
Characteristic function      80 81 102 340
Chronogeometry      120
Clifford group      3 9 325
Clopen set      332
Closed linear hull      332
Closed operator      48
Closed-convex hull      120
Cobb — Douglas production function      350 351
Code      268
Codeword      268 269 270
Codeword length      268 269 270
Coding theorem, source (noiseless)      268 70
Coding theory      267
Collineation, collinearity      77 78
Combinatorics      202 367 377
commodities      352
Completely additive number theoretical, function      372
Completely monotonic function      138
Complex functions      52 53 66 98 130 148 150 153 155 162 209 237 336 338 343 367
Composite functional equations      3 320 326 327 374
Conditional expectation      334
Conditional functional equation      41 73 75 79 80 82 91 105 186 191 265 373 374 377 conditional)
Cone      115 118 120 121 127 128 136 161 257
Congruential inequalities      71
Contiguous extension      335
Continuous solution of a functional equation      15 18 22 23 26 29 30 2 35 36 38 41 43 48 50 53 70 81 83 101 103—5 107 108 111 13 115 117 20 127 128 133 134 139 186 191 194 243 245 7 251 255 258 259 271 284 285 291 4 296 297 308 312 15 320 322 324—6 330 340 2 346 361 362 365 367—9 371
Contour line representation      298 300
Convex hull      120 130
Convex set, cone      115 118 120 130
Convolution      92 102 155
Cost      353
Cylinder type functional equation      261 263 266 274
Darboux property      128
Decision theory      378
Derivation operator      337 338 339
Derivation, derivation equation      23 39 320 338 339
Diagonal matrix      40 41 341
diamond      87 88 90 92
Dilogarithm      9 377
Dirac measure      134 147
Direction (of vectors)      2 105
Discontinuous      18 23 65 71 79 121 124 6 128 290 362 372
Domain of a functional equation      11 18 28 30 73 88 103 213 214 216 236 239 273 282 345 372 373 377
Dual topological group      110 112 55
Dyadic fraction      105 288 90
Dynamical system      377
d’Alembert’s equation      5 103 105 107 9 112 209 220 222 225 363 364 366
Economic effectiveness      346 347 353
Economics      346 348 351 3 378
Elliptic geometry      108
Encoder      269
Endomorphism      57 59 70 71 83 372 376
Entire function      69 339 370
Entropy, entropies of rank a, of order a      28 268 269
Epimorphism      262 266 326 328
Equivalent valuation      285
Euclidean geometry      105 108
Euler function      265
Euler’s equation      324
Euler’s partial differential equation      354 362
Event      27 66 73 120 201 207
Exave      336 337
Exponential mean      240 245 248 50 268
Exponential polynomial      237
Extension (extend)      11 20 26 29 31 58 85 89 91 98 100 101 152 4 266 273 290 291 337 349 373
Extreme operator      135
Extreme point      129 130 3 137 138 146 147 161
Extreme ray      137 138 161
F-linear function      251
F-locally additive      284 285
Fibre bundle      337
Fixed point method      79
Fourier integral      97 98
Fourier transform      97 110 111
Free group      83
Fubini’s Theorem      93
Full set      88
Functional      60 61 97 135 151
Functional analysis      60 129 331 377 378
Functional equation with a restricted domain      73 373
Fundamental equation of information      68 69
Fundamental theorem of algebra      59
Fundamental theorem of projective geometry      371
Gas dynamics      191
Gauss’s functional equation      32
General solution of a functional equation      18 19 26 27 29 32 35 36 38 40 42—4 48 53 54 56 60 67 69 82 83 86 105 120 194 195 204 10 212 214 17 219 222 225 226 230 238 242 243 245 251 257 263 271 281 291 294 7 308 315 320 329 346 347 353 354 362 364 369 372 376 377 continuous)
Generalized groupoid      302 303 5 307
Generalized quasigroup      302 303 8
Generating function      206
Geometric mean      240 245 249
Geometrical optics      74
Graph of a function      14 15 20 128 256 257
Group      2
Group divisible by      2 2 3 217 19 225 237 238 251
Group of periods      3 6 330
Groupoid      42 43 46 48 114 210 12 225 240 242 250 302
Haar measure      102 109 154 163 237 263 284
Hamel basis      18 19 21 24 57 124 6 265 277 371 372
Harmonic analysis      60 66 92 98 108 110 129 156 378
Harmonic mean      245
Hausdorff space      37 130 134 146 147 149 152 162 331 3 335 337 338
Hausdorffs maximality theorem      58 59
Heaviside function      81
Hermitian      168 171 4
Hermitian matrix      39
Hexagonal condition (H)      307 308
Homeomorphism      147 150 151 153 162 252
Homogeneity      201 348 349 352 353 362
Homogeneity equation      345
Homogeneity, generalized      345 348 349
Homogeneity, partially generalized      348
Homogeneous linear purely differential, geometric object      39 41
Homomorphism      83 98 102 113 119 149 151 153 162 242 263 267 285 316
Hua’s theorem      83
Hyperbolic geometry      108
Hyperstonean space      331
Hypothesis H      230
Ideal gas      191 192
Idempotence      288
Incompressible fluid      330
Infinitesimal generator      47
information      27 66 73
Information measure      66
Information theory      27 267 378
Inner product      167 183 190 195 228
Inner product space      129 167 168 178 185 186 190 191 195
Input quantities (variables)      348 349
Internal      243 245 247
Interpolating operator      334 335
Interpolator      334 335 336
Irreducible and monic polynomial      59
Isometry      142 144 7 153 154
Isomorphic      112 132 150 151 153 154 162 303 307 317 331 333
Isotopic, isotopism, isotopy      303 304 306 8
Iteration theory      377
Iterative convex decomposition      341
Jacobian matrix      39
Jacobi’s elliptic cosine function      238
Jensen convex functions, Jensen inequality      127 128 136 242
Jensen equation      142 242 248 255 356
Kernel      76 77 116
Kraft inequality      268 270 271
Krein — Milman theorem      130 138
Kronecker theorem      64 71
L-independent      236
Laplacian      330
Lebesgue integral      55 92 235 8
Lebesgue measure      16 18 20 21 24 37 38 49 50 56 94 6 99 102 121 124—6 128 169 236 8 263 284 340 371
Length of a vector      2 105 106
Lie method      309
Lifting      262 263 267 283 310 317 326 9 341 342
Linear dependence      23 228 229
Linear extension operator      335 336
Linear form      37 154
Linear independence      14 71 72 141 228 230 232 6
Linear operator      36 48 130 2 195 330 331 333 334 336 338 343
Linear operator of composition      336
Liouville’s theorem      339
Lobachevskii’s equation      22 83 111
Locally compact Abelian group      66 98 108 110 113 154 155 163 237 263
Locally convex space      38
Logarithm      360 361 366
Loop      305 304 305 307 308
Lorentz transformation      120
Marginal returns      351 352
Markov condition      20 202 336 337
Markov processes      201
Maximum output      348
Maxwell — Boltzmann distribution law      165 193 194 198
Meager set      265 286 371
Measurable function      26 55 57 128 371
Measurable set      24
Measure theory      114
Mediality (bisymmetry)      8 107 287 293 5 298
Mediality, generalized      298 305
Medians      178
Merton theorem      357
Mikusinski equation      75
Monoid      43 114 342
Monotonic function      15 18 20 119 242 245 8 266 270 271 273 6 278 279 281 4 287 290 7 308 320 348 353 371 373
Moufang loop      307
Multiplace function      298 307 345 367 376
Multiplicative functional      93 102 339
Multiplicative mapping      97 148
Multiplicative operator      130
Multiplicatively symmetric operator      356 337 343
Navier — Stokes equation      330
Newtonian fluid      330
Nice operator      35 147
Nomogram      298 300
Nomography      298
Nonarchimedian valuation      158 163
Noneuclidean geometry and mechanics      105 373
Nonnegative operator      130 132
Nonsingular      128
Nonsingular matrix      39 40 77
Norm      47 118 132 133 152 155 165 190 191 339
Normal distribution      32 370
Normed spacc      36 38 47
Number theory      61 265
One parameter subgroup      113 309
Order generated by a cone      115
Order preserving      115 116 18
Order reversing      115 118
Orthogonal additivity      186 189
Orthogonally rich      190 191
Output      353
p-adic valuation      57 158
Parallel anamorphosis      300
Parallel nomogram      300 301
Parallelogram of forces      1
Parallelogram rule      105 364
Partial differential equation      330 331 362
Partial differential equation, nonlinear      330
Period, set of periods      3 316 328 330 3
Pexider equation      42 57 100 120 240 25 298 300 340 0
Physics      359 363 365 378
Poisson distribution      206 207
Poisson process      207
Pontryagin’s theorem      155
Positive definite      110
Precedence relation      120
Price      352
Price index      352
probability      27 66 201 207 268 270 334 376 378
Probability distributions      206 377
Production function      348 349 351
Production process      346 348
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