Note that, since Fk is real valued, we can also represent Fk by
∞
(A.35)
Fk(x) α α0,k + Σ (αj,kcos(2 π jχ) + βj,ksin(2 π jχ)),
where
co,k = αo,k ; for j ≥ 1: cj
α ., - i β ,
J,k J,k
-------ɔ-------, cj, k
α ., + i β ,
J, k ,i, k
2
(A.36)
Since
∫exp(2iπjχ)dχ III(■=0),
(A.37)
it follows that
F(x)dx O 0 implies c0,k - α0,k - 0,
(A.38)
hence
Fk(x ) = Σ cj, keχp(2 i π jx )∙
Next, observe that
(A∙39)
x
0
i π jy ) dy =
eχp(2 iπjχ) - 11(j.≠0)
2 i ∏ j
÷ xI(j'=0)
(A∙40)
and
x
Jy exp(2 i π jy ) dy =
0
λx exp(2 i π jx)
ч 2iπj
exp(2 i π jx) - 1
(2 i π j )2
ʌ
I(j'≠0)
√
÷ -2x21(j' 0),
(A∙41)
hence, for j1 ≠ 0, j2 ≠ 0,
44
More intriguing information
1. A Brief Introduction to the Guidance Theory of Representation2. WP 36 - Women's Preferences or Delineated Policies? The development or part-time work in the Netherlands, Germany and the United Kingdom
3. Philosophical Perspectives on Trustworthiness and Open-mindedness as Professional Virtues for the Practice of Nursing: Implications for he Moral Education of Nurses
4. The Clustering of Financial Services in London*
5. Climate change, mitigation and adaptation: the case of the Murray–Darling Basin in Australia
6. Skill and work experience in the European knowledge economy
7. Testing Panel Data Regression Models with Spatial Error Correlation
8. The Tangible Contribution of R&D Spending Foreign-Owned Plants to a Host Region: a Plant Level Study of the Irish Manufacturing Sector (1980-1996)
9. Ultrametric Distance in Syntax
10. The name is absent