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Bhatia R. — Fourier Series (Mathematical Association of America Textbooks)
Bhatia R. — Fourier Series (Mathematical Association of America Textbooks)

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Название: Fourier Series (Mathematical Association of America Textbooks)

Автор: Bhatia R.


This is a concise introduction to Fourier series covering history, major themes, theorems, examples and applications. It can be used to learn this subject, and also to supplement, enhance and embellish undergraduate courses on mathematical analysis.
The book begins with a brief summary of the rich history of the subject over three centuries. The subject is presented in a way that enables the reader to appreciate how a mathematical theory develops in stages from a practical problem (such as conduction of heat) to an abstract theory dealing with concepts such as sets, functions, infinity and convergence. The abstract theory will provide unforeseen applications in diverse areas.
The book begins with a description of the problem that led Fourier to introduce his famous series. The mathematical problems this leads to are discussed rigorously. Examples, exercises and directions for further reading and research are provided, along with a chapter that provides material at a more advanced level suitable for graduate students. The author demonstrates applications of the theory as well as a broad range of problems.
Exercises of varying levels if difficulty are scattered throughout the book. These will help readers test their understanding of the material.

Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2005

Количество страниц: 120

Добавлена в каталог: 09.04.2010

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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 $L_{1}$ functions      85
Fourier coefficients of $L_{2}$ 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, $L_{2}$ 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 $C^{1}$      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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