Related papers: A Slightly Improved Bound for the KLS Constant
A rigorous way to obtain sharp bounds for Stokes constants is introduced and illustrated on a concrete problem arising in applications.
In this paper, we obtain a sharp upper bound for the sum of the first $k$-th eigenvalues for this Dirichlet problem of poly-Laplacian with any order, which is viewed as an extension of the result due to Cheng and Wei (Journal of…
Olkin [3] obtained a neat upper bound for the determinant of a correlation matrix. In this note, we present an extension and improvement of his result.
A criterion is presented for the Modified Logarithmic Sobolev inequality on metric measure spaces. The criterion based on U-bound inequalities introduced by Hebisch and Zegarlinski allows to show the inequality for measures that go beyond…
We introduce a new technique proving formula size lower bounds based on the linear programming bound originally introduced by Karchmer, Kushilevitz and Nisan [11] and the theory of stable set polytope. We apply it to majority functions and…
We prove new endpoint bounds for the lacunary spherical maximal operator and as a consequence obtain almost everywhere pointwise convergence of lacunary spherical means for functions locally in $L\log\log\log L(\log\log\log\log…
We show that one can obtain logarithmic improvements of $L^2$ geodesic restriction estimates for eigenfunctions on 3-dimensional compact Riemannian manifolds with constant negative curvature. We obtain a $(\log\lambda)^{-\frac12}$ gain for…
We improve constants in the Rademacher-Menchov inequality.
Under the Riemann Hypothesis, we improve the error term in the asymptotic formula related to the counting lattice problem studied in a first part of this work. The improvement comes from the use of Weyl's bound for exponential sums of…
We obtain a new bound in the uniform version of the Glasner property for matrices with polynomial entries, improving that of K. Bulinski and A. Fish (2021). This improvement is based on a more careful examination of complete rational…
The explicit semiclassical treatment of the logarithmic perturbation theory for the bound-state problem of the radial Shrodinger equation with the screened Coulomb potential is developed. Based upon h-expansions and new quantization…
We establish a lower bound for the complexity of multiplying two skew polynomials. The lower bound coincides with the upper bound conjectured by Caruso and Borgne in 2017, up to a log factor. We present algorithms for three special cases,…
In 1974, Erd\H{o}s and Kleitman conjectured that if a family $\mathcal{F}\subseteq 2^{[n]}$ contains no matching of size \(s\) and is maximal with respect to this property, then $ |\mathcal{F}|\ge \left(1-2^{-(s-1)}\right)\cdot 2^{n}. $ For…
In this paper we obtain further improvement of index bounds for character sums of polynomials over finite fields. We present some examples, which show that our new bound is an improved bound compared to both the Weil bound and the index…
If $(M,g)$ is a compact Riemannian manifold of dimension $n\ge 2$ we give necessary and sufficient conditions for improved $L^p(M)$-norms of eigenfunctions for all $2<p\ne p_c=\tfrac{2(n+1)}{n-1}$, the critical exponent. Since improved…
In this paper we obtain a new constant in the P\'{o}lya-Vinogradov inequality. Our argument follows previously established techniques which use the Fourier expansion of an interval to reduce to Gauss sums. Our improvement comes from…
The upper estimates for the optimal constants of the multilinear Bohnenblust--Hille inequality obtained in [J. Funct. Anal. 264 (2013), 429--463] are here improved to: {0.1cm} {enumerate} For real scalars:…
We compare and combine two approaches that have been recently introduced by Dafnis and Paouris [DP] and by Klartag and Milman [KM] with the aim of providing bounds for the isotropic constants of convex bodies. By defining a new hereditary…
We provide a sufficient condition for a measure on the real line to satisfy a modified logarithmic Sobolev inequality, thus extending the criterion of Bobkov and G\"{o}tze. Under mild assumptions the condition is also necessary.…
For the quadratic Lagrange interpolation function, an algorithm is proposed to provide explicit and verified bound for the interpolation error constant that appears in the interpolation error estimation. The upper bound for the…