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Boundary value problems and controllability of linear systems with right invertible operators

Nguyen Van Mau — 1992

CONTENTSIntroduction..........................................................................................................................................................5Preliminaries........................................................................................................................................................7   1. Linear spaces and linear operators..............................................................................................................7   2. Right...

On solutions of integral equations with analytic kernels and rotations

Nguyen Van MauNguyen Minh Tuan — 1996

Annales Polonici Mathematici

We deal with a class of integral equations on the unit circle in the complex plane with a regular part and with rotations of the form (*)     x(t) + a(t)(Tx)(t) = b(t), where T = M n , k . . . M n m , k m and M n j , k j are of the form (3) below. We prove that under some assumptions on analytic continuation of the given functions, (*) is a singular integral equation for m odd and is a Fredholm equation for m even. Further, we prove that T is an algebraic operator with characteristic polynomial P T ( t ) = t ³ - t . By means of the Riemann boundary value...

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