Related papers: Variation and oscillation inequalities for convolu…
We investigate stationarity and stability of half-spaces as isoperimetric sets for product probability measures, considering the cases of coordinate and non-coordinate half-spaces. Moreover, we present several examples to which our results…
We formulate uncertainty relations for arbitrary $N$ observables. Two uncertainty inequalities are presented in terms of the sum of variances and standard deviations, respectively. The lower bounds of the corresponding sum uncertainty…
In this paper, we got some refinements of the norm inequalities related to the Heinz mean and logarithmic mean.
We find conditions which guarantee moment (in)determinacy of powers and products of nonnegative random variables. We establish new and general results which are based either on the rate of growth of the moments of a random variable or on…
Quantile aggregation with dependence uncertainty has a long history in probability theory with wide applications in finance, risk management, statistics, and operations research. Using a recent result on inf-convolution of quantile-based…
We present new bounds for the Berezin number inequalities which improve on the existing bounds. We also obtain bounds for the Berezin norm of operators as well as the sum of two operators.
In the present paper, the variances in the space and momentum domains of the spherical Abel-Poisson wavelet, as well as the limit of the uncertainty product for $\rho\to0$, where $\rho$ is the scale parameter, are computed. The values of…
In this note, first we refine Mandl's inequality. Then, we consider the product $p_1p_2... p_n$ and we refine some known lower bounds for it, and we find some upper bounds for it by using Mandl's inequality and its refinement and the…
We derive both numerically and analytically Bell inequalities and quantum measurements that present enhanced resistance to detector inefficiency. In particular we describe several Bell inequalities which appear to be optimal with respect to…
The Lorentz covariant tempered disributions with the supports in the product of the closed upper light cones are described.
A variation of multiple $L$-values, which arises from the description of the special values of the spectral zeta function of the non-commutative harmonic oscillator, is introduced. In some special cases, we show that its generating function…
This paper develops a new divergence that generalizes relative entropy and can be used to compare probability measures without a requirement of absolute continuity. We establish properties of the divergence, and in particular derive and…
We compute the involutive knot invariants for pretzel knots of the form P(-2,m,n) for m and n odd and greater than or equal to 3.
We obtain convolution inequalities in Lebesgue and Lorentz spaces with power weights when the functions involved are assumed to be radially symmetric. We also present applications of these results to inequalities for Riesz potentials of…
We find new bi-Lipschitz invariants for functions of two complex variables.
We consider the convolution operator for a measure supported on complex curves. The measure which we consider here is an analogue of the affine arclength measure for real curves. By modifying a combinatorial argument called the band…
This paper considers convolution equations that arise from problems such as measurement error and non-parametric regression with errors in variables with independence conditions. The equations are examined in spaces of generalized functions…
Poisson wavelets are a powerful tool in analysis of spherical signals. In order to have a deeper characterization of them, we compute their uncertainty product, a quantity introduced for the first time by Narcowich and Ward in~\cite{NW96}…
We define a $\mathbb{Z}_2$-valued invariant for transversely-intersecting coassociative $4$-folds equipped with spin structures. Our main result shows this invariant provides an obstruction to separating two such coassociatives through a…
A quantitative version of Minkowski sum, extending the definition of $\theta$-convolution of convex bodies, is studied to obtain extensions of the Brunn-Minkowski and Zhang inequalities, as well as, other interesting properties on Convex…