Some results on biorthogonal polynomials.
Ruedemann, Richard W. (1994)
International Journal of Mathematics and Mathematical Sciences
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Ruedemann, Richard W. (1994)
International Journal of Mathematics and Mathematical Sciences
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Govil, N.K. (2002)
Journal of Inequalities and Applications [electronic only]
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James McKee, Chris Smyth (2013)
Open Mathematics
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We give a complete classification of all pairs of cyclotomic polynomials whose zeros interlace on the unit circle, making explicit a result essentially contained in work of Beukers and Heckman. We show that each such pair corresponds to a single polynomial from a certain special class of integer polynomials, the 2-reciprocal discbionic polynomials. We also show that each such pair also corresponds (in four different ways) to a single Pisot polynomial from a certain restricted class,...
Milovanović, G.V., Rančić, L.Z. (1995)
Publications de l'Institut Mathématique. Nouvelle Série
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K. Dewan, Sunil Hans (2009)
Annales UMCS, Mathematica
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If P(z) is a polynomial of degree n, having all its zeros in the disk [...] then it was shown by Govil [Proc. Amer. Math. Soc. 41, no. 2 (1973), 543-546] that [...] In this paper, we obtain generalization as well as improvement of above inequality for the polynomial of the type [...] Also we generalize a result due to Dewan and Mir [Southeast Asian Bull. Math. 31 (2007), 691-695] in this direction.
Hugh L. Montgomery (1975-1976)
Séminaire Delange-Pisot-Poitou. Théorie des nombres
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Govil, N.K. (1991)
International Journal of Mathematics and Mathematical Sciences
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K. Dewan, Sunil Hans (2008)
Annales UMCS, Mathematica
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If p(z) be a polynomial of degree n, which does not vanish in |z| < k, k < 1, then it was conjectured by Aziz [Bull. Austral. Math. Soc. 35 (1987), 245-256] that [...] In this paper, we consider the case k < r < 1 and present a generalization as well as improvement of the above inequality.
Nikolov, Geno (1999)
Journal of Inequalities and Applications [electronic only]
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Arty Ahuja, K. Dewan, Sunil Hans (2011)
Annales UMCS, Mathematica
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In this paper we obtain certain results for the polar derivative of a polynomial [...] , having all its zeros on [...] which generalizes the results due to Dewan and Mir, Dewan and Hans. We also obtain certain new inequalities concerning the maximum modulus of a polynomial with restricted zeros.
Inoue, Tetsuo (1996)
International Journal of Mathematics and Mathematical Sciences
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Radoš Bakić (2013)
Publications de l'Institut Mathématique
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Thomas Bloom, Jean-Paul Calvi (1999)
Annales Polonici Mathematici
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We prove several new results on the multivariate transfinite diameter and its connection with pluripotential theory: a formula for the transfinite diameter of a general product set, a comparison theorem and a new expression involving Robin's functions. We also study the transfinite diameter of the pre-image under certain proper polynomial mappings.
Gutman, Ivan (1985)
Publications de l'Institut Mathématique. Nouvelle Série
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Mhaskar, H.N. (1991)
International Journal of Mathematics and Mathematical Sciences
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