3 citations · 6 across the 7 of their papers we have counts for
8 papers
The royal road to automatic noncommutative real analyticity, monotonicity, and convexity
J. E. Pascoe, Ryan Tully-Doyle
It was shown classically that matrix monotone and matrix convex functions must be real analytic by Löwner and Kraus respectively. Recently, various analogues have been found in sev…
Noncommutative Schur-type products and their Schoenberg theorem
J. E. Pascoe
Schoenberg showed that a function such that positive semi-definite implies that is also positive semi-d…
Committee spaces and the random column-row property
J. E. Pascoe
A committee space is a Hilbert space of power series, perhaps in several or noncommuting variables, such that Such a space satisfies the true col…
The wedge-of-the-edge theorem: edge-of-the-wedge type phenomenon within the common real boundary
J. E. Pascoe
The edge-of-the-wedge theorem in several complex variables gives the analytic continuation of functions defined on the poly upper half plane and the poly lower half plane, the set…
The noncommutative Löwner theorem for matrix monotone functions over operator systems
J. E. Pascoe
Given a function Löwner's theorem states is monotone when extended to self-adjoint matrices via the functional calculus, if and only if e…
Positivstellensatzë for noncommutative rational expressions
J. E. Pascoe
We derive some Positivstellensatzë for noncommutative rational expressions from the Positivstellensatzë for noncommutative polynomials. Specifically, we show that if a noncommutati…