The Banach spaces of the multiplicative automorphic forms

The multiplicative measurable automorphic forms concerning group, which is isomorphic to Fuchsian group of the first kind and uniformizes a compact Riemann surface, are considered. A norm, a bilinear pairing, the multiplicate operators and functionals in the spaces of the multiplicative measurable and holomorphic automorphic forms of any character are introduced. The continuous embedding the spaces of the multiplicate automorphic forms in space of the single-valued forms of higher order is constructed.