4. Fourier Series Flashcards
1
Q
Definition 4.1
Trigonometric polynomials.
Fourier series.
Real form.
transform from real to complex
A
2
Q
Lemma 4.2
Orthogonality of the trigonometric monomials.
A
3
Q
Formal calculus
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4
Q
Theorem 4.3
Optimality of the Fourier coefficients
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5
Q
Derivation of Bessel’s inequality
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6
Q
Parseval’s Equality
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7
Q
Lemma 4.4
Reimann-Lebesque
Proof
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8
Q
Lemma 4.5
Sin and cos series.
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9
Q
Definition 4.6
Notion of convergence.
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10
Q
Definition 4.7
Dirichlet kernel.
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11
Q
Theorem 4.8
Pointwise convergence of Fourier series.
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12
Q
Lemma 4.9
Decay of Fourier coefficients.
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13
Q
Proposition 4.10
Uniform convergence of Fourier series.
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14
Q
Theorem
Uniform convergence and derivatives.
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15
Q
Theorem 4.11
Regulatiry of the Fourier series.
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