Palabras clave
productos internos del tipo Sobolev
polinomios de Jacobi
comportamiento asintótico
ceros
Cómo citar
Resumen
Consideremos el siguiente producto interno de tipo Sobolev (p, q) = ∫ p(x)q(x)(1 - x)^α(1 + x)^βdx + i[p'(1)q(1) - p(1)q'(1)], donde p y q son polinomios con coeficientes reales, α, β > -1, P(x) = (p(x), q(x))', y A = [M0, M1; M1, M2] es una matriz positiva semidefinida, donde M0, M1 ≥ 0, y A ∈ ℝ. La familia de los polinomios ortogonales con respecto a (1), P_n^{(α,β)}, se llaman polinomios del tipo Jacobi Sobolev. Una expresión que relaciona esta familia de polinomios con P_n^{(0,0)}, los polinomios ortogonales de Jacobi usuales, se obtuvo en [8]. Aquí obtenemos la asintótica relativa exterior para P_n^{(0,0)}, así como también la correspondiente fórmula de Mehler-Heine.
Referencias
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