DruryArveson

DruryArveson refers to the Drury–Arveson space, a canonical object in functional analysis and operator theory. It is a reproducing kernel Hilbert space defined on the open unit ball B_d in C^d and is named for the mathematicians Drury and Arveson who introduced and studied this multivariable generalization of the Hardy space.

Its reproducing kernel is K(z,w) = 1/(1 - ⟨z,w⟩), where ⟨z,w⟩ is the standard Hermitian inner product. This choice of kernel makes the Drury–Arveson space the natural setting for questions in several complex variables and multivariable operator theory. The space supports a distinguished commuting tuple of shift operators, forming a universal model for contractive operator tuples (row contractions) and connecting to dilation and interpolation theory, such as multivariable Nevanlinna-Pick problems.

Research on DruryArveson intersects with multiplier algebras, function theory on the unit ball, and noncommutative function theory. It is cited in discussions of lifting theorems, operator algebra representations, and invariant subspaces, and it continues to influence studies in multivariable operator theory and complex analysis.

Notes: The term may appear in literature as shorthand for the space and its associated operator-theoretic framework. See also: Hardy space, Arveson space, Nevanlinna-Pick interpolation, operator theory.