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

Abstract In this work we study what call Siegel–dissipative vector of commuting operators $$(A_1,\ldots , A_{d+1})$$ ( A 1 , … d + ) on a Hilbert space $${{\mathcal {H}}}$$ H and obtain von Neumann type inequality which involves the Drury–Arveson DA Siegel upper half-space {U}}}$$ U . The operator $$A_{d+1}$$ is allowed to be unbounded it infinitesimal generator contraction semigroup $$\{e^{-i\tau A_{d+1}}\}_{\tau <0}$$ { e - i ? } < 0 We then $$e^{-i\tau A_{d+1}}A^{\alpha }$$ ? where $$A^{\alpha }=A_1^{\alpha _1}\cdots A^{\alpha _d}_d$$ = ? for $$\alpha \in {\mathbb N}_0^d$$ ? N prove that can studied by means model weighted $$L^2$$ L 2 space. To our results Paley–Wiener theorem investigate some multiplier as well.