Plurisubharmonic extension in non-degenerate analytic polyhedra.

Åhag, Per; Czyż, Rafał; Lodin, Sam; Wikström, Frank

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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 $T = M_{n ₁, k ₁} . . . M_{n_{m}, k_{m}}$ 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...