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| Bhatia R. — Fourier Series (Mathematical Association of America Textbooks) |
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| Предметный указатель |
Abel limit 28
Abel summability 28
Algebra 89
Approximate identity 21
Banach algebra 89
Banach space 48
Band matrices 105
Basel problem. 75
Bernoulli numbers 65
Bessel’s inequality. 81
Boundary value problem 15
Cauchy — Schwarz inequality 81
Cesaro summability 28
Convolution 20 85
Convolution and Fourier coefficients 89
Convolution and smoothness 44 90
Convolution, lack of an indentity for 90
Cotangent 62
Dido’s problem 100
Dirac family 22
Dirac sequence 21
Dirichlet kernel 29
Dirichlet problem 15
Dirichlet problem, solution 23
Dirichlet problem, uniqueness of solution 24
Dirichlet’s Theorem 43
Ergodic principle 95
Euler constant 33
Exponential polynomials 33
Fejer kernel 31
Fejer’s theorem 31
Fourier coefficients of  functions 85
Fourier coefficients of  functions 81
Fourier coefficients with respect to an orthonormal system 81
Fourier coefficients, convolution 88
Fourier coefficients, order of magnitude of 40
Fourier coefficients, rate of decay 91
Fourier coefficients, relation with smoothness 43
Fourier coefficients, uniqueness of 24
Fourier series 19 28 31
Fourier series and closest approximation 82
Fourier series, convergence of 79
Fourier series, cosine series 51 52
Fourier series, definition 19
Fourier series, divergence of 46
Fourier series, examples 55
Fourier series, exponential form 52
Fourier series, pointvvise convergence of 35
Fourier series, termwise integration. 45
Fourier series, trigonometric form. 52
Fubini’s Theorem 86
Function on T 19
Function, absolutely continuous 44
Function, bounded variation 41
| Function, even and odd 51
Function, integrable 26
Function, Lipschitz continuous 38
Function, periodic 19
Function, piecewise  36
Gibbs phenomenon 70
Harmonic function 19
Hausdorff moment theorem 53
Heaviside function 57
Hilbert space 79
Infinite products 61
Integrable function 25
Isopcrimctric problem 98
Jordan’s Theorem 43
Korovkin’s theorem 74
Laplace equation solution of 19
Lebesgue constants 33
Legendre polynomials 83
Newton’s Law of Cooling 13
Newton’s Second Law 101
Norm 105
Parseval’s relations 83
Permutation matrix 106
Pinching 107
Plancherel’s theorem 82
Poisson integral 20
Poisson kernel 20
Poisson’s theorem 23
Positive definite sequence 73
Positive operator 74
Principle of localisation 38
Pulse function 55
Rapidly decreasing 84
Riemann — Lebesgue lemma 36 88
Riesz — Fischer theorem 83
Saw-tooth curve 57
Separation method 17
Steady flow of heat 13
Tchebychev polynomial 53
Temperature, maximum and minimum 25
Temperature, mean value property 25
Tonelli’s Theorem 86
Triangular truncation operator. 109
Triangular wave 57
Uniform boundedness principle 48
Unitary matrix 105
Vibrating string 101
Wallis formula. 65
Wave equation. 101
Weierstrass approximation theorem 25 53
Weyl’s Equidistribution Theorem 97
Weyl’s theorem. 96
Wirtinger’s inequality 85
Zeta function 67
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