J"Fk( x )Fm (x )dx "
Σ c1kc-1.
≠0
∞
IV α..α
2*-~' j. k j
> 1
∞
IV β-frβ .
2 .1,k' m,k
(A.46)
Finally.
∖χF∖(* ) dx - ∑
j j≠0
2iπj
“ β t
V l,.k
2π ⅛ j
(A.47)
Q.E.D.
Proof of Lemma 7: Note that the set of solutions of eigenvalue problem (34) is a subset of the
set of solutions of eigenvalue problem
det
m
RqTrC(1)∑ xkxlτc(1) TRq
k= 1
Ï
O
O
√
Y1
Yl
(A.48)
m
RqTrC(1)∑ XkXkTC(1) TR.
= 0,
q-r
√
k= 1
because the matrix in (34) is singular only if the matrix in (A.48) is singular. Moreover. the non-
zero eigenvalues of (A.48) are just the solutions of the eigenvalue problem
det RqTrC(1)∑ XtXkTC(1) R
k= 1
q-r
(
m
- λ RqTrC(1)£ XkXkTC(1)TRι
k= 1
Y1
q-r
y
0 0.
(A.49)
Therefore. the non-zero solutions of eigenvalue problem (34) are bounded from below by the
minimum solution of eigenvalue problem (A.49). and so is T1.m(H). Using the notation (18). it
is easy to verify that this minimum solution is the squared minimum solution of the eigenvalue
problem
46
More intriguing information
1. Social Irresponsibility in Management2. The name is absent
3. Bird’s Eye View to Indonesian Mass Conflict Revisiting the Fact of Self-Organized Criticality
4. The name is absent
5. The name is absent
6. The name is absent
7. EU Preferential Partners in Search of New Policy Strategies for Agriculture: The Case of Citrus Sector in Trinidad and Tobago
8. The name is absent
9. Towards Teaching a Robot to Count Objects
10. The name is absent