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| Авторизация |
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| Поиск по указателям |
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| Wall H.S. — Analytic Theory of Continued Fractions |
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| Предметный указатель |
Polynomials with roots in given circle 190
Polynomials, bounds for moduli of roots 191
Polynomials, changes in sign of 244
Polynomials, computation of roots of 185ff
Polynomials, convex set containing roots 176
Polynomials, Legendre 344
Polynomials, number of roots in half-plane 182
Polynomials, orthogonal relative to sequence 195
Polynomials, rectangle containing roots 177
Polynomials, roots in unit circle 298
Polynomials, test-fraction 174
Polynomials, whose roots are in half-plane 178
Porter 105
Positive definite continued fraction 67
Positive definite continued fraction of Stieltjes type 125
Positive definite continued fraction with partial numerator zero 72
Positive definite continued fraction, bounded reciprocal of J-matrix 233
Positive definite continued fraction, bounds for approximants 72
Positive definite continued fraction, connection with parabola theorem 75
Positive definite continued fraction, denominators not zero 67 72
Positive definite continued fraction, determinate case 110
Positive definite continued fraction, indeterminate case 104
Positive definite continued fraction, lemma on 70
Positive definite continued fraction, nest of circles 71
Positive definite continued fraction, parametric representation 67
Positive definite continued fraction, particular cases of 69
Power series expansion of J-fraction 197 203
Power series expansion of J-fraction, convergence to value of J-fraction 208
Power series expansion of J-fraction, related to J-matrix 228
Power series expansion of J-fraction, related to moment problem 263
Power series expansion of S-fraction 202
Power series expansion of S-fraction, convergence to value of S-fraction 208
Power series solution of differential equation 360 361
Pringsheim 36 48 50
Probability integral 357 358
Pseudo-elliptic integrals 36
Quadratic form, bounded 222
Quadratic form, chain sequences 86
Quadratic form, imaginary part positive 66
Quadratic form, lemma on 332
Quadratic form, positive definite 88
Quadratic form, value of 223
Radius  74 75
Rational function with simple poles and positive residues 167
Rational function, J-fraction for 162
Rational function, Stieltjes type continued fraction for 170
Real analytic functions 277 278
Real analytic functions in Ext  279
Real J-fractions as Stieltjes transform 255
Real J-fractions of norm less than or equal to unity 115
Real J-fractions of norm N 115
Real J-fractions, convergence of 114
Real J-fractions, even part of S-fraction 121
Real J-fractions, nature of poles 114
Real J-fractions, partial fraction development 115
Real J-fractions, roots of denominators 114
Reciprocal of arbitrary J-matrix 229
Reciprocal of arbitrary J-matrix, indeterminate case 230
Reciprocal of arbitrary J-matrix, symmetric 230
Reciprocal of bounded J-matrix 226
Reciprocal of bounded J-matrix, leading coefficient of 228
Reciprocal of J-matrix for positive definite J-fraction 233
Rectangle containing roots 177
Riesz, F. 239 275
Riesz, M. 238
Rogers 204
Roots of polynomial 177 185
Routh’s method 182
S-fraction 200
S-fraction, equal to power series 208
S-fraction, power series expansion of 201
S-fraction, representing meromorphic function 209
Schoenberg 267
schur 285
Schwarz’s inequality 94
Schwerdtfeger 36
Scott 29 48 58 61 123 400 409
Sequences of analytic functions, convergence continuation theorem 108
| Sequences of analytic functions, equi-continuous 107
Sequences of analytic functions, uniformly bounded 105
Sequences of monotone functions 246
Sequences of Stieltjes integrals 245
Shohat 239
Stieltjes 101 104 118 202 210 238 239 245
Stieltjes convergence theorem 120 134
Stieltjes criterion for real J-fraction 121
Stieltjes expansion theorem 203
Stieltjes integrals 239ff.
Stieltjes integrals for analytic functions with positive real parts 275
Stieltjes integrals of polynomials 244
Stieltjes integrals, existence theorem 241 257
Stieltjes integrals, integration by parts 240
Stieltjes integrals, positive 244
Stieltjes integrals, reduction to Riemann integral 241
Stieltjes integrals, sequences of 245
Stieltjes integrals, vanishing 243
Stieltjes inversion formula 250
Stieltjes moment problem 327
Stieltjes moment problem, Carleman’s theorem on 330
Stieltjes moment problem, determinate 329
Stieltjes summability 362
Stieltjes transform 247
Stieltjes transform, inversion of 250
Stieltjes transform, representing equivalent functions of J-fractions 253
Stieltjes type continued fractions 119
Stieltjes type continued fractions for rational functions 171
Stieltjes type continued fractions, condition (H) for 122 131
Stieltjes type continued fractions, convergence of 120
Stieltjes type continued fractions, partial fraction development of 120
Stone 214
Summability, Borel 415
Summability, Cesaro 301 309 310
Summability, de la Vallee Poussin 280
Summability, Euler — Knopp 309
Summability, Hausdorff 301
Summability, Holder 310
Summability, inclusion 305
Summability, mutually consistent 300
Summability, regular 300
Summability, Stieltjes 362
Szasz 18 42 51 143
Tamarkin 239
Test-fraction, algorithm 175
Test-fraction, determinant conditions for 176 190
Theorem of invariability 96
toeplitz 214
Totally monotone sequences 267
Totally monotone sequences, bounded functions 284
Totally monotone sequences, composition of 269
Tschebycheff 192
Two-circle theorem 148
Uniform convergence of continued fraction 16
Uniformly bounded sequences 105
Value of continued fraction 16
Value of continued fraction in circular domain 42 46 60 150
Value of continued fraction on interior of domain 151
Value region problem 146
Value region problem, element region in neighborhood of origin 150
Value region problem, minimal solution 146
Value region problem, parabolic element region 152ff
Value region problem, solution (E,V) of 146
Value region problem, sufficient condition for solution 147
Value region problem, two-circle theorem 148
Value region problem, unique boundary values 151
Van Vleck, E. B. 42 48 131 138 210 238
Verbeek 51
Vitali 105
Volterra sum equation 96
von Koch 27 33 51 143
wall 27 29 31 44 48 51 58 61 69 70 79 98 123 137 178 235 400 409
Weierstrass 45
Wetzel 70
Weyl 96
Widder 239
Worpitzky 42 58
Worpitzky circle 58
Worpitzky’s theorem 42
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