The problem is solved by minimizing a functional depending on the eigenvalues and traces of corresponding eigenmodes.
Depending on the eigenvalues λ k, the number of different spectrograms that are averaged could be just a few or an infinite number.
The difference between two solutions belonging to different weighted Sobolev spaces is a finite linear combination of singular functions depending on the eigenvalues of A and on the corresponding eigenspaces.
We show that if G consists of eigenvectors of the modular operator Δφ with finite free Fisher information, then the centralizer Mφ is a II1 factor and M is either a type II1 factor or a type IIIλ factor, 0<λ≤1, depending on the eigenvalues of G. Furthermore, (Mφ)′∩M= C, Mφ does not have property Γ, and M is full provided it is type IIIλ, 0<λ<1.
In such scenarios, their sum rate performance is similar to the one achieved by approaches depending on the eigenvalue computation.
Equation (24) only depends on the eigenvalues of the covariance function and not on the properties of the local distributions.
It is interesting to ask how this pre-factor depends on the eigenvalues of the trace-class operator Q defining the Q-Wiener process.
But he only gave the reconstruction formula for the energy (q_{0}) and the formula depends on the eigenvalues and nodal lengths.
end{aligned}Then, the matrix difference equation (10) takes the form Y_{k+1}=FY_k+left[ begin{array}{c}0_{omega,1} vdots 0_{omega,1} Gend{array}right].The stability of the above system depends on the eigenvalues of F. Let (lambda) be an eigenvalue of F.
In the work of [16], the authors show that the trajectory of the tap‐weight vector, x 1, depends on the eigenvalues of the equivalent autocorrelation matrix projected on a spreading code subspace orthogonal to the desired user.
