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.

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Post-print Article

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Copyright © 1993 Springer Basel AG.

DOI: 10.1007/978-3-0348-8581-2_10

The definitive version is available at: https://link.springer.com/chapter/10.1007/978-3-0348-8581-2_10

Full Citation:

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.