We show that uniform asymptotics of orthogonal polynomials on the real line imply uniform asymptotics for all their derivatives. This is more technically challenging than the corresponding problem on the unit circle. We also examine asymptotics in the L 2 norm.
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∗Research supported by NSF grant DMS0400446 and US-Israel BSF grant 2004353. Key words and phrases: derivatives of orthogonal polynomials, asymptotics of orthogonal polynomials, Szeg®'s condition. 2000 Mathematics Subject Classification: primary 42C05, 42C99, secondary 41A60.
- Asymptotics of orthogonal polynomials
- Derivatives of orthogonal polynomials
- Szego's condition