The Drury–Arveson Space on the Siegel Upper Half-space and a von Neumann Type Inequality.

In this work we study what we call Siegel–dissipative vector of commuting operators (A 1 , ... , A d + 1) on a Hilbert space H and we obtain a von Neumann type inequality which involves the Drury–Arveson space DA on the Siegel upper half-space U . The operator A d + 1 is allowed to be unbounded and it is the infinitesimal generator of a contraction semigroup { e - i τ A d + 1 } τ < 0 . We then study the operator e - i τ A d + 1 A α where A α = A 1 α 1 ⋯ A d α d for α ∈ N 0 d and prove that can be studied by means of model operators on a weighted L 2 space. To prove our results we obtain a Paley–Wiener type theorem for DA and we investigate some multiplier operators on DA as well. [ABSTRACT FROM AUTHOR]