Díaz Mendoza, C.; Orive, R.; Pijeira Cabrera, H. Zeros and logarithmic asymptotics of Sobolev orthogonal polynomials for exponential weights. (English) Zbl 1177.42020 J. Comput. Appl. Math. 233, No. 3, 691-698 (2009). The authors study the problem of location and asymptotics of zeroes of polynomials orthogonal on the half-axis \(\mathbb{R}^1_+\) with respect to the inner product of the weighted Sobolev space \(W^{2,M}(w,\mathbb{R}^1_+)\) with weight of form \(w(x)=x^\gamma e^{\varphi(x)}, \;\gamma>0\). The obtained asymptotics covers in particular the cases of Freud and Erdös weights. Reviewer: Stefan G. Samko (Faro) Cited in 3 Documents MSC: 42C05 Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis Keywords:Sobolev orthogonal polynomials; zero location; asymptotiv behaviour; exponential weights PDFBibTeX XMLCite \textit{C. Díaz Mendoza} et al., J. Comput. Appl. Math. 233, No. 3, 691--698 (2009; Zbl 1177.42020) Full Text: DOI References: [1] Díaz Mendoza, C.; Orive, R.; Pijeira, H., Asymptotically extremal polynomials with respect to varying weights and application to Sobolev orthogonality, J. Math. Anal. Appl., 346, 480-488 (2008) · Zbl 1155.33006 [2] Duran, A.; Saff, E., Zero location for nonstandard orthogonal polynomials, J. Approx. Theory, 113, 127-141 (2001) · Zbl 1011.42013 [3] Martínez Finkelshtein, A., Analytic aspects of Sobolev orthogonal polynomials revisited, J. Comput. Appl. Math., 127, 255-256 (2001) · Zbl 0971.33004 [4] Marcellán, F.; Moreno, J. J., Asymptotics and zeros of Sobolev orthogonal polynomials on unbounded supports, Acta Appl. Math., 94, 163-192 (2006) · Zbl 1137.42312 [5] López Lagomasino, G.; Marcellán, F.; Pijeira, H., Logarithmic asymptotics of contracted Sobolev extremal polynomials on the real line, J. Approx. Theory, 143, 62-73 (2006) · Zbl 1106.41031 [6] Geronimo, J. S.; Lubinsky, D. S.; Marcellán, F., Asymptotics for Sobolev orthogonal polynomials for exponential weights, Constr. Approx., 22, 3, 309-346 (2005) · Zbl 1105.42016 [7] Levin, E.; Lubinsky, D. S., Orthogonal polynomials for exponential weights \(x^{2 \rho} e^{- 2 Q(x)}\) on \([0, d)\), J. Approx. Theory, 134, 199-256 (2005) · Zbl 1079.42017 [8] Levin, E.; Lubinsky, D. S., Orthogonal polynomials for exponential weights \(x^{2 \rho} e^{- 2 Q(x)}\) on \([0, d)\), II, J. Approx. Theory, 139, 107-143 (2006) · Zbl 1127.42023 [9] Levin, E.; Lubinsky, D. S., (Orthogonal Polynomials for Exponential Weights. Orthogonal Polynomials for Exponential Weights, CMS Books in Mathematics, vol. 4 (2001), Springer-Verlag: Springer-Verlag New York) · Zbl 0997.42011 [10] Rakhmanov, E. A., On asymptotic properties of polynomials orthogonal on the real axis, Math. USSR Sb., 47, 155-193 (1984) · Zbl 0522.42018 [11] Saff, E.; Totik, V., Logarithmic potentials with external fields, (Grundlehren der Mathematischen Wissenschaften. Grundlehren der Mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics, vol. 316 (1997), Springer-Verlag: Springer-Verlag Heidelberg) · Zbl 0881.31001 [12] Knopfmacher, A.; Lubinsky, D. S., Analogues of Freud’s conjecture for Erdös type weights and related polynomial approximation problems, (Lecture Notes in Math., vol. 1287 (1987), Springer: Springer Berlin), 21-69 · Zbl 0638.41009 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.