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Rogosinski W. — Fourier Series
Rogosinski W. — Fourier Series



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Название: Fourier Series

Автор: Rogosinski W.

Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1950

Количество страниц: 176

Добавлена в каталог: 17.04.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$\mathfrak{U}$-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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