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Sharp Turán inequalities via very hyperbolic polynomials
(2011-04-15)
We present new sharp inequalities for the Maclaurin coefficients of an entire function from the Laguerre-Pólya class. They are obtained by a new technique involving the so-called very hyperbolic polynomials. The results ...
Sharp Turán inequalities via very hyperbolic polynomials
(2011-04-15)
We present new sharp inequalities for the Maclaurin coefficients of an entire function from the Laguerre-Pólya class. They are obtained by a new technique involving the so-called very hyperbolic polynomials. The results ...
Distances between critical points and midpoints of zeros of hyperbolic polynomials
(Gauthier-villars/editions Elsevier, 2010-03-01)
Let p(x) be a polynomial of degree n with only real zeros x(1) <= x(2) <= ... <= x(n). Consider their midpoints z(k) = (x(k) + x(k+1))/2 and the zeros xi(1) <= xi(2) <= ... <= xi(n-1) of p'(z). Motivated by a question posed ...
Another connection between orthogonal polynomials and L-orthogonal polynomials
(Elsevier B.V., 2007-06-01)
We consider a connection that exists between orthogonal polynomials associated with positive measures on the real line and orthogonal Laurent polynomials associated with strong measures of the class S-3 [0, beta, b]. ...
Another connection between orthogonal polynomials and L-orthogonal polynomials
(Elsevier B.V., 2007-06-01)
We consider a connection that exists between orthogonal polynomials associated with positive measures on the real line and orthogonal Laurent polynomials associated with strong measures of the class S-3 [0, beta, b]. ...
Distances between critical points and midpoints of zeros of hyperbolic polynomials
(Gauthier-villars/editions Elsevier, 2010-03-01)
Let p(x) be a polynomial of degree n with only real zeros x(1) <= x(2) <= ... <= x(n). Consider their midpoints z(k) = (x(k) + x(k+1))/2 and the zeros xi(1) <= xi(2) <= ... <= xi(n-1) of p'(z). Motivated by a question posed ...
Distances between critical points and midpoints of zeros of hyperbolic polynomials
(Gauthier-villars/editions Elsevier, 2014)
Another connection between orthogonal polynomials and L-orthogonal polynomials
(Elsevier B.V., 2014)
Robust Non-Hyperbolic Fibred Quadratic Pplynomial Dynamics
(Amer. Inst. Mathematical Sciences-AIMS, 2023)
We consider the dynamics of fibred quadratic polynomials over an irrational rotation of the circle. We construct a simple mechanism, so-called critical connection, that implies non-hyperbolicity. To exhibit that critical ...