JxFk(x)dx о 0, (28)
respectively, and to verify afterwards that the optimal weight functions Fk satisfy the stronger
conditions (6) and (7).
Without loss of generality we may represent the functions Fk by their Fourier flexible
form
∞∞
Fk(x) α αo,k + ∑ αj,kcos(2jπx) + ∑ βj,ksin(2jπx)
Then by some tedious but straightforward calculations it can be shown that:
Lemma 6. The conditions (27), (28), (8), (9), and (10) now read as:
Fk(χ)dχ α αok - 0

;(χ)dχ - -F-∑ β
2π J=1 J
ffFk(x )Fm (y )min(x, y ) dxdy
8π2

÷Σ
J=1
βJ,kβJ,
0 if k ≠ m ,
∞
F(x ) [Fm (y ) dydx = -r- Σ
4 4 4 П 7=1
β
J, kt^J, m
Vj-1
∞
Σ
j=1
β
J,m J,k
[Fk(x )Fm (x ) dx = ʌ
∞
V α..α.
X-7 j, k j,
Ij'1
ʌ
-∞
÷ βjkβ rnt
0 if k ≠ m .
Combining (1) and the results of Lemma 6, we have
16
More intriguing information
1. The Dictator and the Parties A Study on Policy Co-operation in Mineral Economies2. The name is absent
3. The name is absent
4. The Social Context as a Determinant of Teacher Motivational Strategies in Physical Education
5. Disentangling the Sources of Pro-social Behavior in the Workplace: A Field Experiment
6. Wirkt eine Preisregulierung nur auf den Preis?: Anmerkungen zu den Wirkungen einer Preisregulierung auf das Werbevolumen
7. Modelling the Effects of Public Support to Small Firms in the UK - Paradise Gained?
8. On the Relation between Robust and Bayesian Decision Making
9. The name is absent
10. Design and investigation of scalable multicast recursive protocols for wired and wireless ad hoc networks