ON MULTIPLICATION OF CONTRAVARIANT SYMBOLS
We introduce a multiplication of contravariant symbols in polynomial quantization on para-Hermitian symmetric spaces. For simplicity, we take a crucial example: the hyperboloid of one sheet in ℝ3. The multiplication is induced by the multiplication of operators. It is defined by an integral. The kernel of this integral gives a transform (an analog of the Berezin transform) which moves covariant symbols to contravariaiit ones. We find an expression of this transform in terms of the Laplace-Beltrami operator. For this algebra of contravariant symbols, the correspondence principle is true.