Let μ and v be regular finite Borel measures with compact support in the real line ℝ and define the differential operator D :L ∞(μ) → L ∞(v) with domain equal to the polynomials P by Dp = p′. In this paper we will characterize the weak-star closure of the graph of D in ∞(μ) ⊕ ∞(y). As a consequence we will characterize when D is closable (i.e. the weak-star closure of G contains no non-zero elements of the form o ⊕ g) and when g is weak-star dense in L∞(μ) ⊕ L ∞(v). We will also consider the same problem where μ and v are measures supported on the unit circle T.
Copyright © 1993 Springer Basel AG.
The definitive version is available at: https://link.springer.com/chapter/10.1007/978-3-0348-8581-2_10
Ross, William T., and Joseph A. Ball. "Weak-Star Limits of Polynomials and Their Derivatives." Contributions to Operator Theory and Its Applications, 1993, 165-75. doi:10.1007/978-3-0348-8581-2_10.
Ross, William T. and Ball, Joseph A., "Weak-star limits on polynomials and their derivatives" (1993). Math and Computer Science Faculty Publications. 183.