Asymptotic upper bounds for the entropy of orthogonal polynomials in the Szegő class.
Ficheros
Identificadores
Compartir
Metadatos
Mostrar el registro completo del ítemFecha
2004Resumen
We give an asymptotic upper bound as $n\to\infty$ for the entropy integral $$E_n(w)= -\int p_n^2(x)\log (p_n^2(x))w(x)dx,$$ where $p_n$ is the $n$th degree orthonormal polynomial with respect to a weight $w(x)$ on $[-1,1]$ which belongs to the Szeg\H{o} class. We also study two functionals closely related to the entropy integral. First, their asymptotic behavior is completely described for weights $w$ in the Bernstein class. Then, as for the entropy, we obtain asymptotic upper bounds for these two functionals when $w(x)$ belongs to the Szeg\H{o} class. In each case, we give conditions for these upper bounds to be attained.
Palabra/s clave
Análisis asintótico
Polinomios ortogonales
Variables aleatorias