Related papers: On the multilinear Bohnenblust--Hille constants: c…
We consider Hardy-Rellich inequalities and discuss their possible improvement. The procedure is based on decomposition into spherical harmonics, where in addition various new inequalities are obtained (e.g. Rellich-Sobolev inequalities). We…
It was recently proved that for $p>2m^{3}-4m^{2}+2m$ the constants of the Hardy--Littlewood inequality for $m$-linear forms on $\ell_{p}$-spaces are less than or equal to the best known estimates of respective constants of the…
Hardy-Littlewood-Sobolev (HLS) Inequality fails in the "critical" case: \mu=n. However, for discrete HLS, we can derive a finite form of HLS inequality with logarithm correction for a critical case: \mu=n and p=q, by limiting the inequality…
We presented here a refinement of Hermite-Hadamard inequality as a linear combination of its end-points. The problem of best possible constants is closely connected with well known Simpson's rule in numerical integration. It is solved here…
Fourier analysis on the discrete hypercubes $\{-1,1\}^n$ has found numerous applications in learning theory. A recent breakthrough involves the use of a classical result from Fourier analysis, the Bohnenblust--Hille inequality, in the…
The optimal constants are found for Lebesgue norm multilinear inequalities of Holder-Brascamp-Lieb type for arbitrary discrete Abelian groups. Previously a criterion for finiteness of the constants had been established for finitely…
We develop a framework to give upper bounds on the "practical" computational complexity of stability problems for a wide range of nonlinear continuous and hybrid systems. To do so, we describe stability properties of dynamical systems using…
We investigate the growth of the polynomial and multilinear Hardy--Littlewood inequalities. Analytical and numerical approaches are performed and, in particular, among other results, we show that a simple application of the best known…
Imagine two parties, Alice and Bob who share an entangled quantum state. A well-established result that if Alice performs two-outcome measurement on the portion of the state in her possession and Bob does likewise, they are able to produce…
We explicitly solve a variational problem related to upper bounds on the optimal constants in the Cwikel--Lieb--Rozenblum (CLR) and Lieb--Thirring (LT) inequalities, which has recently been derived in [Invent. Math. 231 (2023), no.1,…
In this paper, we will prove a very general result of stability for perturbations of linear integrable Hamiltonian systems, and we will construct an example of instability showing that both our result and our example are optimal. Moreover,…
Previous noncommutative Bohnenblust--Hille (BH) inequalities addressed operator decompositions in the tensor-product space $M_2(\mathbb{C})^{\otimes n}$; \emph{i.e.,} for systems of qubits \cite{HCP22,VZ23}. Here we prove noncommutative BH…
To estimate the optimal constant in Hardy-type inequalities, some variational formulas and approximating procedures are introduced. The known basic estimates are improved considerably. The results are illustrated by typical examples. It is…
The Cahn-Hilliard equation is related with a number of interesting physical phenomena like the spinodal decomposition, phase separation and phase ordering dynamics. On the other hand this equation is very stiff an the difficulty to solve it…
In a generalization of the classical Hilbert inequality by Hardy, Littlewood and P\'{o}lya, the best constant for an inequality is determined provided that the generating function for the corresponding matrix satisfies certain monotonicity…
We use an interpolative technique from \cite{abps} to introduce the notion of multiple $N$-separately summing operators. Our approach extends and unifies some recent results; for instance we recover the best known estimates of the…
When analysing extreme values, two alternative statistical approaches have historically been held in contention: the block maxima method (or annual maxima method, spurred by hydrological applications) and the peaks-over-threshold. Clamoured…
There are increasingly suggestions for computer simulations of quantum statistics which try to violate Bell type inequalities via classical, common cause correlations. The Clauser-Horne-Shimony-Holt (CHSH) inequality is very robust.…
This work is devoted to the development of a novel theoretical approach, named hybrid approach, to handle a localized bottleneck in a symmetrically coupled two-channel totally asymmetric simple exclusion process with Langmuir kinetics. The…
In this article we consider the inhomogeneous incompressible Euler equations describing two fluids with different constant densities under the influence of gravity as a differential inclusion. By considering the relaxation of the…