|
|
 |
| Авторизация |
|
|
|
| Поиск по указателям |
|
|
|
|
|
|
|
 |
|
|
|
| Widder D.V. — The Laplace transform |
|
|
|
| Предметный указатель |
Karamata 189 191
Karamata's theorem 189
Kernels of positive type 270
Kernels, positive 270
Kernels, positive, definite 270
Kernels, positive, semidefinite 271
Knopp 264
l'Hospital's rule 79
l.i.m. 80 245
Laguerre polynomials 168
Laguerre polynomials, Laplace transform of 170
Lambert series 231
Landau 49 56 64 99 193 195
Laplace 277
Laplace integral, convergence properties of the 38
Laplace integral, integration by parts of the 41 239
Laplace integral, uniform convergence of the 53
Laplace kernel, general representation theorem for 302
Laplace kernel, integral equation with 390
Laplace method, applications of the 280
Laplace method, uniform convergence 283
Laplace transform of Laguerre polynomials 170
Laplace transform,  -  for the 47
Laplace transform, abscissa of convergence of 37 38 42
Laplace transform, abscissa of uniform convergence of the 51
Laplace transform, absolute convergence of the 46
Laplace transform, axis of convergence of the 37
Laplace transform, axis of uniform convergence of the 50
Laplace transform, bilateral 237
Laplace transform, complex inversion formula for the 63
Laplace transform, Condition A for 306
Laplace transform, Condition A' for 308
Laplace transform, Condition B for 312
Laplace transform, Condition C for 315
Laplace transform, Condition D for 317
Laplace transform, inversion formula for 386
Laplace transform, inversion formula of 276
Laplace transform, iteration of the 325
Laplace transform, jump operator for 298
Laplace transform, region of convergence of the 35
Laplace transform, representation by 276
Laplace transform, uniform convergence of the 50
Laplace transform, unilateral 35
Laplace transform, uniqueness of the 80
Laplace transforms, Abelian theorems for the 180
Laplace — Lebesgue transform, inversion operator for the 288
Laplace — Lebesgue transform, transforms, product of 91
Laplace — Stieltjes integral, inversion formula for the 69
Laplace — Stieltjes transform 37
Laplace — Stieltjes transform, general 320
Laplace — Stieltjes transform, inversion operator for the 290
Laplace — Stieltjes transforms, product of 88
Laplace's asymptotic evaluation of an integral 277 296
Lattice points 228
Law of the mean 108
Laws of the mean for Stieltjes integrals 16
Least upper bound 4
Lebesgue set 78 244 289 345
Lebesgue — Stieltjes integral 4 20
Lebesgue's limit theorem 97 104 260
Leibniz's rule 295 351
Lerch 61
Limit in the mean 80
Limit in the mean, theorem, Lebesgue's 97
Linear functional 105 171
Linear functional, as Stieltjes integral 105
Liouville 71
Lipschitz condition 72 75
Little moment problem 100
Littlewood 71 193 195 198 199 370
Logarithmically convex functions 167
Lower bound, greatest 4
Mathias 273
Matrix, diagonal 114
Matrix, difference 114
Matrix, Hausdorff 118 119
Matrix, theory 113
Max, true 34
Maximal type 94
Mean convergence 81
Mean square convergence 245
Measurable functions 11
mellin 246
Mellin transform 246
Mellin — Stieltjes transform 246
Mercer 270 271
Mertens 89
Method of summability (C,p) 121
Method of summability (H,p) 120
Method of summability stronger 121
Methods of summability, consistent 115
Methods of summability, equivalent 121
Methods of summability, permanent 115
Methods of summability, regular 115
Minimal completely monotonic sequence 163
Minimal type 94
Mittag — Leffler development 97 261
Moment function, of a polynomial 102 127
Moment function, operator 102 126
Moment function, uniqueness of 60
Moment operator, extension of 127
Moment operator, problem 100
Moment operator, problem, indeterminacy of solution of 142
Moment operator, problem, little 100
Moment operator, problem, of Hamburger 125
Moment operator, problem, of Hausdorff 100
Moment operator, problem, of Stieltjes 136
Moment operator, sequence 100 101
Moment operator, sequence, Condition B for 109
Moment operator, sequence, Condition C for 111
Moment operator, sequence, necessary and sufficient conditions for 103
Moment operator, sequences, inversion operator for 107
Moments of functions of bounded variation 138
Necessary and sufficient conditions for representation as a bilateral Laplace transform 272
NOERLUND 97
Non-decreasing determining Amotion 310
Non-decreasing functions 6
Non-vanishing of the zeta-function 229
Norm 4
Norm, of a function of class A 205
Normal orthogonal set 168
Normal type 94
Normalization of functions of bounded variation 13
Normalized determining function 237
Number theoretic functions 224
One-sided derivatives of absolutely monotonic functions, existence of 149
One-sided derivatives of absolutely monotonic functions, Tauberian theorem 215
Operational considerations 381
Order conditions 357
Order conditions of an entire function 94 179
Order conditions on vertical lines 92
Order conditions, properties of the determining function 38
Orthogonal set, normal 368
Osgood 260 261 389
Parseval theorem 81 202
Periodic determining function 96
Permanent 115
Permanent, methods of summability 115
Pincherle 37
Pitt 210 216
Pitt's form of Wiener's theorem 210
Plancherel's Theorem 81 202
Point of increase 6
Point of invariability 6 19
Pollard 289 295
Polya 138 172 229 370
Polynomial, Bernstein 101
Polynomials, positive 132 172
Positive definite kernels 270
Positive definite quadratic forms 135
| Positive definite sequences 132
Positive kernels 270
Positive polynomials 132 172
Positive quadratic forms 166
Positive semidefinite kernels 271
Positive semidefinite sequences 132
Positive sequences 127 159 266
Positive type, kernels of 270
POST 276 289
Power series, product of 88
Prime-number theorem 224 236
Product of bilateral Laplace integrals 252 257
Product of Fourier transforms 203
Product of Fourier — Stieltjes transforms 252
Product of Laplace — Lebesgue transforms 91
Product of Laplace — Stieltjes transforms 88
Product of power series 88
Properties of Stieltjes integrals 8 12
Quadratic forms 273
Quadratic forms, definite 136
Quadratic forms, positive 166
Quadratic forms, positive, definite 135
Quadratic forms, semidefinite 136
Quotient of Fourier transforms 207
Region of convergence of the bilateral Laplace transform 23S
Region of convergence of the Laplace transform 35
Region of convergence of the Stieltjes transform 326
Regular 115
Regular, methods of summability 115
Relation between the Laplace transform and the Stieltjes transform 334
Representation by the bilateral Laplace transform 265
Representation by the Laplace transform 276
Resultant, bilateral Stieltjes 248
Resultant, unilateral Stieltjes 83
Riemann 66 71 246
Riemann integral 4
Riemann — Lebesgue theorem 65 68 77 83 207 235
Riemann — Stieltjes integral 4
Riemann-integrable functions 180
Riesz 105 127
Rolle's theorem 168
Saks 26 324
Saltus 299
Schoenberg 105
Second law of the mean, Bonnet's 17
Selection principle, the 26
Semidefinite quadratic forms 136
Semidefinite sequences 132
Semidefinite sequences, positive 132
Sequence of functions of uniformly bounded variation 31
Sequence, completely monotonic 158 269
Sequence, minimal completely monotonic 163
Sequence, positive 127 159 266
Sequence, positive definite 132
Sequence, positive semidefinite 132
Sequence, semidefinite 132
Series of absolutely monotonic functions 151
Shohat 135
Singular integral 341
Singular point of the Stieltjes transform 336
Singularities of the generating function 58
Slowly decreasing functions 209
Slowly oscillating functions 209
Solution of an integral equation 357
Special Tauberian theorem 209
Step-function 6
Stieltjes 125 126 325 338
Stieltjes integral as a Lebesgue integral 11
Stieltjes integral as a Lebesgue series 10
Stieltjes integral, absolutely convergent improper 15
Stieltjes integral, change of variable of 19
Stieltjes integral, conditions of integrability for the 24
Stieltjes integral, equation 387
Stieltjes integral, integration by parts for the 8
Stieltjes integral, linear functional as 105
Stieltjes integral, Tauberian theorem for the 213
Stieltjes integral, variation of the indefinite 20
Stieltjes integrals 3
Stieltjes integrals as infinite series 22
Stieltjes integrals, convergent improper 15
Stieltjes integrals, divergent improper 15
Stieltjes integrals, existence of 7
Stieltjes integrals, improper 15
Stieltjes integrals, inequalities for 9
Stieltjes integrals, integration with respect to an indefinite 12
Stieltjes integrals, iterated 25
Stieltjes integrals, laws of the mean for 16
Stieltjes integrals, properties of 8 12
Stieltjes integration of series 10
Stieltjes kernel, general representation theorem for 355
Stieltjes kernel, integral equation with 387
Stieltjes kernel, iterates of the 259 262
Stieltjes moment problem 136
Stieltjes moment problem, not unique 125
Stieltjes moment problem, sufficient condition for the solubility of the 140
Stieltjes resultant 83
Stieltjes resultant, at infinity 86 247
Stieltjes resultant, bilateral 249 250
Stieltjes resultant, of indefinite integrals 256
Stieltjes resultant, variation of 85
Stieltjes transform 325
Stieltjes transform, Abelian theorems for the 183
Stieltjes transform, analytic character of 328
Stieltjes transform, complex inversion formula 335
Stieltjes transform, conditions A for 361
Stieltjes transform, conditions B for 369
Stieltjes transform, conditions C for 372
Stieltjes transform, conditions D for 374
Stieltjes transform, elementary properties of the 325
Stieltjes transform, general representation theorems for the 360
Stieltjes transform, inversion operator for the 345 347
Stieltjes transform, jump operator for 351
Stieltjes transform, region of convergence of 326
Stieltjes transform, relation to the Laplace transform 334
Stieltjes transform, singular at the origin 336
Stieltjes transform, singular point of 336
Stieltjes transform, Tauberian theorems for the 198
Stieltjes transform, uniqueness of 336 349
Stieltjes transform, variation of  for 353
Stieltjes transforms, asymptotic properties of 329
Stirling's formula 95 227 231 281 352
Stolz region 240
Stronger method of summability 121
Subdivision 3
Sufficient condition for the solubility of the Stieltjes moment problem 140
Summability by a matrix 114
Summability of bilateral Laplace transform 244
Summability of divergent integrals 75
Summability, (C,p), method of 121
Summability, equivalent methods of 121
Summability, stronger method of 121
Summable (C,1) 79 244
Szegoe 168 169 172 229
Tamarkin 21 63 113 163
Tauber 186 188
Tauberian theorem 321
Tauberian theorem for the Stieltjes integral 213
Tauberian theorem, complex variable 233
Tauberian theorem, one-sided 215
Tauberian theorem, special 209
Tauberian theorem, Wiener's general 212
Tauberian theorems 180 185
Tauberian theorems for the Stieltjes transform 198
Taylor's formula 146 179 278
Taylor's series 267
Taylor's theorem 177 193
Titchmarsh 6 81 97 314 338 341 387 389
toeplitz 115
Toeplitz's theorem 115 119
Total variation 6
|
|
|
| Реклама |
|
|
|
|
|
|
|
|
О проекте