Abstract
The main purpose of this work is to realize and establish the extension of a noether operator A defined by a third kind singular integral equation. The extended operator of the initial operator A is noted  and acting from a new specific functional space constructed denoted Vm=C−11−11⊕∑k=1mαkF.p1xk, into the same previous space C0P−11. We investigate the noetherity of the extended initial noether operator noted Â, when we realized the extension taking the unknown function φx from the spaceVm. The index of such noether operator χ is calculated and therefore, the conditions of the noetherity nature of the extended operator are established.
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