Journal
INTERNATIONAL MATHEMATICS RESEARCH NOTICES
Volume 2022, Issue 8, Pages 5935-5972Publisher
OXFORD UNIV PRESS
DOI: 10.1093/imrn/rnaa249
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Funding
- National Science Foundation [DMS-1147523, DMS-1464479, DMS-1764245]
- Van Vleck Professorship Research Award
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This article considers the continuous dependence of weighted operators on L-p(R-d) space, and uses this result to estimate the norm of orthogonal polynomials on the unit circle. Additionally, the asymptotics of polynomial entropy is obtained as an application.
We consider weighted operators acting on L-p(R-d) and show that they depend continuously on the weight w is an element of A(p) (R-d) in the operator topology. Then, we use this result to estimate L-w(p)(T) norm of polynomials orthogonal on the unit circle when the weight w belongs to Muckenhoupt class A(2)(T) and p > 2. The asymptotics of the polynomial entropy is obtained as an application.
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