resolvent kernel

resolvent kernel

[ri′zäl·vənt ′kər·nəl]
(mathematics)
A function appearing as an integrand in an integral representation for a solution of a linear integral equation which often completely determines the solutions.
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The proof of the theorem is done by constructing the resolvent kernel R([zeta]; [H.sub.d])(x,y) with the spectral parameter [zeta] [member of] [D.sub.d].
The second step is to construct the resolvent kernel with two solenoids for the pair ([d.sub.-], [d.sub.0]) by composing two resolvent kernels with one solenoid.
The third step is to construct the resolvent kernel of the operator [H.sub.d] in question from the two kernels corresponding to the two centers ([d.sub.-], [d.sub.0]) and to one center [d.sub.+].