Access

You are not currently logged in.

Access your personal account or get JSTOR access through your library or other institution:

login

Log in to your personal account or through your institution.

If You Use a Screen Reader

This content is available through Read Online (Free) program, which relies on page scans. Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.

Polynomial Approximation with Varying Weights on Compact Sets of the Complex Plane

Igor E. Pritsker
Proceedings of the American Mathematical Society
Vol. 126, No. 11 (Nov., 1998), pp. 3283-3292
Stable URL: http://www.jstor.org/stable/119144
Page Count: 10
  • Read Online (Free)
  • Download ($30.00)
  • Subscribe ($19.50)
  • Cite this Item
Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Polynomial Approximation with Varying Weights on Compact Sets of the Complex Plane
Preview not available

Abstract

For a compact set E with connected complement, let A(E) be the uniform algebra of functions continuous on E and analytic interior to E. We describe A(E,W), the set of uniform limits on E of sequences of the weighted polynomials {Wn(z)Pn(z)}$_{n=0}^{\infty} $, as n → ∞ , where W ∈ A(E) is a nonvanishing weight on E. If E has empty interior, then A(E,W) is completely characterized by a zero set Z$_{W}\subset $ E. However, if E is a closure of Jordan domain, the description of A(E,W) also involves an inner function. In both cases, we exhibit the role of the support of a certain extremal measure, which is the solution of a weighted logarithmic energy problem, played in the descriptions of A(E,W).

Page Thumbnails

  • Thumbnail: Page 
3283
    3283
  • Thumbnail: Page 
3284
    3284
  • Thumbnail: Page 
3285
    3285
  • Thumbnail: Page 
3286
    3286
  • Thumbnail: Page 
3287
    3287
  • Thumbnail: Page 
3288
    3288
  • Thumbnail: Page 
3289
    3289
  • Thumbnail: Page 
3290
    3290
  • Thumbnail: Page 
3291
    3291
  • Thumbnail: Page 
3292
    3292