Small values of polynomials: Cartan, Pólya and others.

Lubinsky, D.S.

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Displaying similar documents to “Small values of polynomials: Cartan, Pólya and others.”

Some results on biorthogonal polynomials.

Ruedemann, Richard W. (1994)

International Journal of Mathematics and Mathematical Sciences

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On growth of polynomials.

Govil, N.K. (2002)

Journal of Inequalities and Applications [electronic only]

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Single polynomials that correspond to pairs of cyclotomic polynomials with interlacing zeros

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,...

An estimate for coefficients of polynomials in $L^{2}$ norm. II.

Milovanović, G.V., Rančić, L.Z. (1995)

Publications de l'Institut Mathématique. Nouvelle Série

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On maximum modulus for the derivative of a polynomial

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.

Polynomials in many variables

Hugh L. Montgomery (1975-1976)

Séminaire Delange-Pisot-Poitou. Théorie des nombres

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Some inequalities for maximum modules of polynomials.

Govil, N.K. (1991)

International Journal of Mathematics and Mathematical Sciences

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Growth of polynomials whose zeros are outside a circle

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.

An inequality for polynomials with elliptic majorant.

Nikolov, Geno (1999)

Journal of Inequalities and Applications [electronic only]

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Inequalities concerning polar derivative of polynomials

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.

Some properties of weighted hyperbolic polynomials.

Inoue, Tetsuo (1996)

International Journal of Mathematics and Mathematical Sciences

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Generalization of the Grace–Heawood Theorem

Radoš Bakić (2013)

Publications de l'Institut Mathématique

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On the multivariate transfinite diameter

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.

On some graphic polynomials whose zeros are real.

Gutman, Ivan (1985)

Publications de l'Institut Mathématique. Nouvelle Série

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Finite-infinite-range inequalities in the complex plane.

Mhaskar, H.N. (1991)

International Journal of Mathematics and Mathematical Sciences

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