Lp Markov–Bernstein Inequalities on Arcs of the Circle
✍ Scribed by D.S. Lubinsky
- Publisher
- Elsevier Science
- Year
- 2001
- Tongue
- English
- Weight
- 142 KB
- Volume
- 108
- Category
- Article
- ISSN
- 0021-9045
No coin nor oath required. For personal study only.
📜 SIMILAR VOLUMES
The converse inequality of Markov type is discussed in this note. The main result says that the best possible constant for this inequality is the square root of the least eigenvalue of a certain positive definite matrix. As applications of the main result, the Laguerre weight and Hermite weight are
Orthogonal polynomials on the unit circle are fully determined by their reflection coefficients through the Szego recurrences. Assuming that the reflection coefficients converge to a complex number a with 0< |a| <1, or, in addition, they form a sequence of bounded variation, we analyze the orthogona
Ratio and relative asymptotics are given for sequences of polynomials orthogonal with respect to measures supported on an arc of the unit circle, where their absolutely continuous component is positive almost everywhere. The results obtained extend to this setting known ones given by Rakhmanov and M
Starting from the Delsarte Genin (DG) mapping of the symmetric orthogonal polynomials on an interval (OPI) we construct a one-parameter family of polynomials orthogonal on the unit circle (OPC). The value of the parameter defines the arc on the circle where the weight function vanishes. Some explici