Then, for a sufficiently large number in modulus [lambda] [member of] [[PHI].sub.[??],[psi]], the inverse operator
[(q - [lambda]I).sup.-1] exists and is continuous in space H = [L.sup.2](0, 1), and the following estimate holds:
Ideally, if one plans to run both power and coupling analysis based on MNE source estimates, two distinct inverse operators
should be implemented.
Thus, we have proved that the operator T has an inverse operator
The main strategy of the method of operator is to find the inverse operator
of the primary differential problem, i.e.
REDUCING THE NUMBER OF INVERSE OPERATORS
IN THE CARTESIAN RULES
By finding the inverse operator
and imposing initial condition we obtain
Therefore, by the inverse operator
theorem, we obtain that [[bar.T].sup.1] is a bounded linear operator.
Apply the inverse operator
, [J.sup.[alpha].sub.t], which is the Riemann-Liouville fractional integral of order [alpha] > 0.
Although their relationship was linked to the general IMC strategy, they apply equally well to the neural network inverse model based IMC strategy here, where the inverse operator
or controller is approximated by the neural network inverse model instead.
where the notation A-1 denotes the inverse operator
for the linear operator A of (18).
In view of (4) and (17), by applying the inverse operator
[I.sup.[alpha]] on both sides of (16) and solving corresponding integrals we get
Generalized Inverse Operators
: And Fredholm Boundary-Value Problems, 2nd Edition