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Integral transforms connected with differential systems with a singularity.

We consider some integral transforms with the kernels expressed in terms of solutions of the system of differential equations \( y'=(x^{-1}A+B)y, \) where \(A\) and \(B\) are constant \(n\times n\), \(n>2\) , matrices. We study analytical and asymptotical properties of such transforms. We also study the transforms as operators acting in some functional spaces.