proposition 17.10 Smoothness and coefficient decay
open in the book ·
parts/02-mathematical-methods/15-fourier-integral-transforms.tex:462
· p. 677
Rests on
- depends_on definition 17.1 Fourier coefficients and Fourier series ¶
- depends_on equation 7.28 eq:ana-parts ¶
-
depends_on
lemma 17.7
Riemann–Lebesgue
¶
-
depends_on
definition 7.39
Darboux sums and the definite integral
¶
- depends_on axiom 7.1 Completeness of $\R$ ¶
- proves proof ch:15-fourier-integral-transforms@proof-5 ¶
-
depends_on
definition 7.39
Darboux sums and the definite integral
¶
- proves proof ch:15-fourier-integral-transforms@proof-8 ¶
Supports
- depends_on corollary 17.11 Uniform convergence for $C^{1}$ functions ¶
Neighborhood
Every logical edge within two steps of this node.
- declared and complete
- partly declared
- a check failed
- not graded
- declared in the source
- inferred from structure
Edges
| type | direction | node | provenance | where |
|---|---|---|---|---|
depends_on |
→ | Fourier coefficients and Fourier series | declared | parts/02-mathematical-methods/15-fourier-integral-transforms.tex:472 |
depends_on |
→ | eq:ana-parts | declared | parts/02-mathematical-methods/15-fourier-integral-transforms.tex:472 |
depends_on |
→ | Riemann–Lebesgue | declared | parts/02-mathematical-methods/15-fourier-integral-transforms.tex:472 |
depends_on |
← | Uniform convergence for $C^{1}$ functions | declared | parts/02-mathematical-methods/15-fourier-integral-transforms.tex:502 |
proves |
← | ch:15-fourier-integral-transforms@proof-8 | declared | parts/02-mathematical-methods/15-fourier-integral-transforms.tex:475 |