HILBERT SPACES UNCONDITIONAL BASES CONSISTING OF VALUES OF ENTIRE VECTOR-FUNCTIONS OF ORDER 1/2

摘要

Let B be a dissipative Volterra operator in a separable Hilbert space h such that the resolvent (I — zB)~(-1) has finite exponential type. A complete description is given of the operators B with the above properties, vectors g ∈ h, and sequences A of complex numbers such that the family (I-λ_kB~2)~(-1), λ_k∈Λ, forms an unconditional basis in h. Bibliography: 8 titles.