Contents vii
Chapter 10. The Fourier Transform 249
10.1. Definition and basic properties 249
10.2. The inversion formula 255
10.3. Fourier transforms in mean square 263
10.4. The Poisson summation formula 270
10.5. Linear combinations of translates 277
Notes 278
Chapter 11. Higher Dimensions 279
11.1. Multiple Discrete Fourier Transforms 279
11.2. Multiple Fourier Series 280
11.3. Multiple Fourier Transforms 286
Notes 290
Appendix B. The Binomial Theorem 291
B.1. Binomial coefficients 291
B.2. Binomial theorems 293
Appendix C. Chebyshev Polynomials 299
Appendix F. Applications of the Fundamental Theorem
of Algebra 309
F.1. Zeros of the derivative of a polynomial 309
F.2. Linear differential equations with constant coefficients 312
F.3. Partial fraction expansions 313
F.4. Linear recurrences 315
Appendix I. Inequalities 319
I.1. The Arithmetic–Geometric Mean Inequality 319
I.2. older’s Inequality 325
Notes 338
Appendix L. Topics in Linear Algebra 339
L.1. Familiar vector spaces 339
L.2. Abstract vector spaces 344
L.3. Circulant matrices 347
Notes 348
Appendix O. Orders of Magnitude 349
Appendix T. Trigonometry 351
T.1. Trigonometric functions in plane geometry 351
T.2. Trigonometric functions in calculus 357
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