On an Unconditional Basis of Generalized Eigenvectors of the Nonself-adjoint Gribov Operator in Bargmann Space

In this article we prove that the system of generalized eigenvectors of the Gribov operator is an unconditional basis in Bargmann space. We also give a generalized diagonalization in the Abel sense.of the semigroups, respectively, associated to this operator and to its square root. Finally, some open problems are pointed out.