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| Rogosinski W. — Fourier Series |
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| Предметный указатель |
 -method 110 118
A-process 104
Abel 110
Abel-Poisson process (see A-process)
Abel’s continuity theorem 19 110
Abschnittskoppelung 128
Absolutely integrable 165
Admissible sequence of subdivisions 162
Analysis, harmonic 43
Arithmetic mean value method (see M-method)
Arzela 149
Arzela — Lebesgue theorem 149
bernoulli 3 19 36 39
Bernoulli, numbers 37
Bernoulli, polynomials 38
Bessel’s inequality 52
Bessel’s inequality, boundary condition 2
Bessel’s inequality, value problem 121
Bounded variation 161
Cauchy criterion 169
Cauchy — Schwarz inequality 167
Cauchy — Schwarz inequality, closed interval 160
Cauchy — Schwarz inequality, system 14 50
Closure theorem 11
Complete system 50
Completeness theorem 53
Conditions, initial 2
Conjugate series 82
Continuity, uniform 160
Continuous function with divergent Fourier series 76 103
Continuous, piecewise 30
Convergence problem 4 64
Convex 25
Courant — Hilbert 50
Criterion, Dini’s 68
Darboux integral 162
Darboux integral, theorem 162
Derivative, generalized second 124 142
Dini’s criterion 68
Dirichlet discontinuous factor 93
Dirichlet integral 64 116
Dirichlet — Jordan criterion 72
Dirichlet’s 18
Dirichlet’s criterion 18
Dirichlet’s criterion, formula 64
Dirichlet’s, Young’s convergence 85
Discontinuous factor, Dirichlet 93
Divergent Fourier series 103
DuBois — Reymond 76
DuBois — Reymond, theorem 147 154
D’Alembert 3 42
Eigenvibration 2
Elastic force 1
Elongation function 1
Equilibrium position 1
Euler 3 6 16 19 28 35 58 61
Euler — MacLaurin series 98
Euler — MacLaurin series, summation formula 96
Even function 11
Fejer 76 103 111
Fejer’s integral 112 116
Fejer’s integral, kernel 116
Fejer’s integral, means 111 121 140
First boundary value, problem 121
Fischer (see Riesz-Fischer)
FOURIER 4 6
Fourier value 88
Fourier, coefficients 6 21
Fourier, condition 88
Fourier, integral theorem 88
Fourier, series 8
Fourier, series, divergent 103
Fourier, series, integration of 26
Fractions, partial 35
frequency 44
Function, even 11
Function, odd 11
Fundamental (mode) 44
Fundamental (mode), generalized second derivative 124 142
Fundamental (mode), interval 8
Gibbs phenomenon 135
Half-open interval 160
Harmonic analysis 43
Hausdorff 149
Heat conduction 88
Heine — Cantor theorem 144
Helmholtz 44
hilbert (see Courant-Hilbert)
Hurwitz 61
Hurwitz, improper integral 164
Hurwitz, improperly integrable 163
Hurwitz, inequality, Bessel’s 52
Hurwitz, initial conditions 2
Hurwitz, position 1
Hurwitz, Schwarz 167
Hurwitz, velocity 1
Improper 164
Improper, Lebesgue 53 149
Improperly 163
Improperly, properly 162
Integrable function 165
Integrable, absolutely 165
integral 162
Integral, Darboux 162
| Integral, Dirichlet 64 116
Integration by parts 163
Integration of Fourier series 26
Intensity of sound 44
Interchange of “lim” and integral sign 149
Interval, closed 160
Interval, half-open 160
Interval, open 160
Isoperimetric problem 61
JORDAN (see Dirichlet - Jordan criterion)
Jordan, arc 61
Jordan, kernel 116
Jordan, theorem 161
Legendre polynomials 7 14 57
Leibniz series 18
Limitation process 108
Linear independence 8
Lipschitz condition 69
Logarithmic potential 121
Logarithmic potential, series 19
Lukacs 83
M-lim (see M-process)
M-process of summation 109 111
Maclaurin (see Euler-MacLaurin)
Matrix, Toeplitz 104
Mean value method, arithmetic (see M-method)
Mean value methods 103
Measure, zero 164
Method of summation (see Summation process)
Minimal property of Fourier series 50
NEAR 160
Normal function 30
Numbers, Bernoulli 37
Odd function 11
Open interval 160
Ordinary point 70 75
Orthogonal system 7
Orthogonality 5
Oscillation of partial sums 132
Overtone 44
Partial fractions 35
periodicity 10
Physical intuition 3
Piecewise continuous 30
Pitch 44
poisson 120 (see A-method)
Poisson, integral 120 121
Poisson, summation formula 96
Polynomials, Bernoulli 38
Polynomials, Legendre 7 14 57
Potential, logarithmic 121
Pringsheim 83
Properly integrable 162
Properly integrable, representation problem 5 10 30
Riemann 43 123
Riemann, method of summation 122 146
Riemann’s lemma 21 52
Riemann’s lemma, theorem 66 83
Riesz — Fischer theorem 54
Saltus 16 134
Schwarz’ inequality 167
Schwarz’ inequality, Euler — MacLaurin 98
Schwarz’ inequality, Leibniz 18
Schwarz’ inequality, logarithmic 19
Schwarz’ inequality, series, conjugate 82
Schwarz’ inequality, theorem 141 142
Sequence, admissible, of subdivisions 162
Set theory 149
Set theory, reducible 147
Sine 3
Sine series 3
Singular point 116 163
Sound 44
square-integrable 166
Steiner 61
Sternberg 121
Stirling’s formula 98 99
Subdivision 161
Summation by parts 16
Summation formula, Euler - MacLaurin 96
Summation formula, Poisson 120 (see A-method)
Summation formulas 95
Summation formulas, method 109
Summation formulas, problem 5 9 18
Summation formulas, process, Lebesgue 122
System, closed 14
System, complete 50
System, orthogonal 7
Term by term integration, differentation 170
Theorem 105
Theorems 141
Timbre 44
Toeplitz matrix 104
Trigonometric series 4 10
Uniform continuity 160
Uniform convergence 168
uniform convergence of Fourier series 6 10
Uniqueness problem 5
Variation, bounded 161
Vibrating string 1 39 88
Wallis formula 101
Wave equation 2
Weber 43
Weierstrass aproximation, theorem 14 46 115
Young’s convergence criterion 85
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