THE INTEGRAL OPERATOR OF PROJECTION AND POINCARE SERIES FOR HOLOMORPHIC (Q; Ρ ) − FORMS

Abstract

The paper addresses the spaces of multiplicate integrable automorphic forms on the plane domain D and on the compact Riemann surface D/G; where the group G is isomorphic to Fuchsian group of the first kind. The paper investi gates the operator of projection of measurable forms onto holomorphic ones and the operator determining Poincare ρ series and translating forms for trivial group into forms for any group G. Universal estimates of norms of these opera tors; the reproduction formula; the self-conjugation and  surjection properties were received.