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Vretblad A. — Fourier Analysis and Its Applications (Graduate Texts in Mathematics)
Vretblad A. — Fourier Analysis and Its Applications (Graduate Texts in Mathematics)

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Название: Fourier Analysis and Its Applications (Graduate Texts in Mathematics)

Автор: Vretblad A.

Аннотация:

A carefully prepared account of the basic ideas in Fourier analysis and its applications to the study of partial differential equations. The author succeeds to make his exposition accessible to readers with a limited background, for example, those not acquainted with the Lebesgue integral. Readers should be familiar with calculus, linear algebra, and complex numbers. At the same time, the author has managed to include discussions of more advanced topics such as the Gibbs phenomenon, distributions, Sturm-Liouville theory, Cesaro summability and multi-dimensional Fourier analysis, topics which one usually does not find in books at this level. A variety of worked examples and exercises will help the readers to apply their newly acquired knowledge.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2003

Количество страниц: 280

Добавлена в каталог: 14.09.2015

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Abel summation      152
Almost ever where      116
Amplitude      76
Angular frequency      90
Autocorrelation function      102 194
Bessel inequality      111 117
Black Box      53 67 239
Boundary condition      10
Boundary values      10 137
Carleson's theorem      89
CD recordning      188
Cesaro summation      20 82 96 97
Chain rule      211
Characteristic curve      6
Chebyshev polynomials      128
Compact support      200
Completeness      111 119
Complex exponential      15
Complex vector space      105
Continuity on T      74
Convergence of distributions      213
Convergence of test functions      20
Convergence, pointwise      86 87 117
Convergence, uniform      12 24 83 117
Convergence, various notions      117
Convolution      53 65 80 176 218 232 239
D'Alembert formula      8
Delta "function"      28 57 96 199 205
Derivative of distribution      208
Difference equation      61
Diffusion equation      1
Dipole      31 226
Dirac "function"      28 57 96 199 205
Dirichlet kernel      81 87 93
Dirichlet problem      145 148
Distance      115
distribution      27 57 96 190 203
Domain      1
Double series      230
Eigenvalue      154
Eigenvdiker      154
Electric Dipole      31 226
Elliptic equation      3
Equality of distributions      206
Equality of functions      115
Euler's formulae      16 17
Even function      77
Expansion theorem      112
Fejer kernel      8
Fejer theorem      82
FFT      243
Fibonacci numbers      64
Fourier coefficients      75 116
Fourier series      75 220
Fourier series, multi-dimensional      233
Fourier transform      165
Fourier transform of distributions      213
Fourier transform, discrete      243
Fourier transform, fast      243
Fourier transform, inversion      171
Fourier transform, multi-dimensional      236
Fundamental tone      144
Fundamenul solution      58 221
Fuzzy point      199 200
Generalized derivative      86
Gibbs phenomenon      93
Heat equation      1 9 137 139 182 223
Heaviside function      29 204
Heaviside window      29 209
Heisenberg principle      198
Hermite polynomials      127 160
Homogeneous condition      10
Hyperbolic equation      2
Impulse response      67 69 240
Initial values      7 10
Inner product      106
Kahane and Katznelson      89
Laguerre polynomials      127 160
Laplage equation      2 145 159 185 223
Laplage operator      1
Laplage transform      28 39 188
Laplage transform, inversion      189
Laplage transform, uniqueness      48
Laurent series      60
Least squares approximation      110
Lebesgue spaces      115
Legendre polynomials      124 159
Mean value      79
Moderately increasing function      201
Modes of vibration      144
Multiplicator      201
Norm      107 115
Odd function      77
ON set      108
Operator      154
Orthogonal      108
Orthogonal projection      110
Orthonormal set      108
P.V.      206
Parabolic equation      2
Parseval formula      112 113 120
Partial tone      141
Partition of unity      203
Phase angle      76
Plangherel formula      180
Point charge      27 198
Pointwise convergence      86 87 117
Poisson equation      2
Poisson kernel      152
Poisson summation      152
Principal value      206
Projection      110
Pulse response      67 69 240
Pulse train      96 220
Residual      111
Resonance      5
Riemann — Lebesgue lemma      25
Rodrigues formula      125 127
Roof function      24
Sampling theorem      187
Separation of variables      10 137
Series, double      230
Series, Fourier      75 220
Series, Laurent      60
Series, rearrangement of      227
Series, summability of      21
Shannon's sampling theorem      187
Spherical harmonics      159
Stability of black box      68 69
Stability of differential equation      4
Sturm — Liouville operator      156
Sturm — Liouville problem      155
Sturm — Liouville problem, singular      158
Sturm — Liouville Theorem      157
Summability of series      21
Summation kernel      22
Support      200 207
Symmetric operator      154
Tempered distribution      203
Tempered function      201
Test function      200
Transfer function      68 69
Tricomi equation      3
Uniform continuity      24 168
Uniform convergence      12 24 83 117
Uniqueness      4 48 84 176
Unit step function      29
Vector space      105
Vibrating string      143
Vibration, modes of      144
Wave equation      2 5 143 211
Weierstrass approximation theorem      124
Weight function      115
Well-posed problem      3
Z transform      60
Zero set      89 116 207 233
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