Integral mean estimates for polynomialis with restricted zeros

Estimates of Multilinear Singular Integral Operators and Mean Oscillation

Zeros of Functions with Finite Dirichlet Integral

In this paper, we refine a result of Nagel, Rudin, and Shapiro (1982) concerning the zeros of holomorphic functions on the unit disk with finite Dirichlet integral. This is a remark about the zeros of functions f = ), n�0 anz holomorphic on U z z < 1} that have finite Dirichlet integral D(f ) := ∞ |f |dA = n|an|, n=0 where dA is Lebesgue measure in the plane. Clearly such functions belong to th...

Improved Asymptotics for Zeros of Kernel Estimates via a Reformulation of the Leadbetter-Cryer Integral

The expected number of false inflection points of kernel smoothers is evaluated. To obtain the small noise limit, we use a reformulation of the Leadbetter-Cryer integral for the expected number of zero crossings of a differentiable Gaussian process.

Some compact generalization of inequalities for polynomials with prescribed zeros

‎Let $p(z)=z^s h(z)$ where $h(z)$ is a polynomial‎ ‎of degree at most $n-s$ having all its zeros in $|z|geq k$ or in $|z|leq k$‎. ‎In this paper we obtain some new results about the dependence of $|p(Rz)|$ on $|p(rz)| $ for $r^2leq rRleq k^2$‎, ‎$k^2 leq rRleq R^2$ and for $Rleq r leq k$‎. ‎Our results refine and generalize certain well-known polynomial inequalities‎.

Integral Transforms of Functions with Restricted Derivatives