Integral transforms connected with differential systems with a singularity.

Abstract

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.

On the Weyl--type solutions of differential systems with a singularity. Case of discontinuous potential

“…with arbitrary R > 0 and Lemma 3.1 from [26] we deduce that (K(q)f )(x, •) ∈ L 2 (l) for any x ∈ [0, ∞) and, moreover,…”

“…From the results of [26] it follows that T 1 k ∈ C X p , BC [0, ∞), C 0 S and, moreover, for any ray {ρ = zt, t ∈ [0, ∞)} with z ∈ S \ {0} the restriction T 1 k l belongs to the space C (X p , BC ([0, ∞), H(l))). I.…”