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Abstract: In this note we give some results of the following type. Let z_j (j=1,...,n) be distinct complex numbers on the unit circle, but not equal to 1. Then the limes inferior of the real parts of ...
Numerically explicit version of the Pólya--Vinogradov inequality
Numerically explicit version the Pólya--Vinogradov inequality
2011/8/23
Abstract: In this paper we proved a new numerically explicit version of the P\'{o}lya--Vinogradov inequality. Our proof is based on the new ideas of V.A. Bykovskii and improves a recent inequality obt...
Hardy inequality and heat semigroup estimates for Riemannian manifolds with singular data
semigroup Riemannian manifolds singular data
2010/11/12
Upper bounds are obtained for the heat content of an open set D in a geodesically complete Riemannian manifold M with Dirichlet boundary condition on bd(D), and non-negative initial condition. We sho...
Some improvements on the constants for the real Bohnenblust-Hille inequality
improvements constants real Bohnenblust-Hille inequality
2010/12/6
A classical inequality due to Bohnenblust and Hille states that for every N ∈ N and every m-linear mapping U : ℓN 1 × · · · × ℓN 1 → C we have N X i1,...,im=1 U(ei1 , ..., eim) 2m m...
A Trace Inequality for Positive Definite Matrices
Trace inequality positive definite matrices positive semidefinite matrices
2010/1/25
In this note we prove that when the following two conditions are met: (i) the matrices are structured as follows , , , (ii) , are positive definite matrices and , are positive semidefinite matric...
A Reverse Hardy-Hilbert-Type Integral Inequality
Hardy-Hilbert-type integral inequality weight function $beta$ function Holder's inequality
2010/1/25
By estimating a weight function, a reverse Hardy-Hilbert-type integral inequality with a best constant factor is obtained. As an application, some equivalent forms and some particular results have be...
A Stability Version of Hölder's Inequality for $0 < p < 1$
Hö lder's inequality Reverse triangle inequality
2010/1/25
We use a refinement of Hölder's inequality for to obtain the corresponding refinement when . This in turn allows us to sharpen the reverse triangle inequality on the nonnegative functions in , f...