Related papers: Variations on the theme of Marcinkiewicz' inequali…
We will formulate and prove a generalization of the isoperimetric inequality in the plane. Using this inequality we will construct an unitary space - and in consequence - an isomorphic copy of a separable infinite dimensional Hilbert space,…
Theory interpolation has found several successful applications in model checking. We present a novel method for computing interpolants for ground formulas in the theory of equality. The method produces interpolants from colored congruence…
Monge-Kantorovich optimal mass transport (OMT) provides a blueprint for geometries in the space of positive densities -- it quantifies the cost of transporting a mass distribution into another. In particular, it provides natural options for…
In this paper we prove a Marcinkiewicz-type multiplier result for the spherical Fourier transform on products of rank one noncompact symmetric spaces.
Some adaptive analogue of the Mirror Prox method for variational inequalities is proposed. In this work we consider the adaptation not only to the value of the Lipschitz constant, but also to the magnitude of the oracle error. This…
An inequality, which combines the concept of completely monotone functions with the theory of divided differences, is proposed. It is a straightforward generalization of a result, recently introduced by two of the present authors.
We provide a complete proof of an optimal version of the Marcinkiewicz multiplier theorem.
A unified approach used to generalize classical Brunn-Minkowski type inequalities to Lp Brunn-Minkowski type inequalities, called the Lp transference principle, is refined in this paper. As illustrations of the effectiveness and…
The purpose of this work is to give a direct proof of the multiplicative Brunn-Minkowski inequality in nilpotent Lie groups based on Hadwiger-Ohmann's one of the classical Brunn-Minkowski inequality in Euclidean space.
We survey some interplays between spectral estimates of H\"ormander-type, degenerate Monge-Amp\`ere equations and geometric inequalities related to log-concavity such as Brunn-Minkowski, Santal\'o or Busemann inequalities.
Ariki's and Grojnowski's approach to the representation theory of affine Hecke algebras of type $A$ is applied to type $B$ with unequal parameters to obtain -- under certain restrictions on the eigenvalues of the lattice operators --…
The present article deals with properties of a certain function of the Minkowski type with arguments defined by Engel series. Differential, integral, and other properties of the function were considered.
We prove an inequality of the form $\gamma_n\geq C_n(\gamma_{n-1})$ giving a lower bound for the Hermite constant $\gamma_n$ in dimension $n$ in terms of $\gamma_{n-1}$. Iterating this inequality yields a new proof of the Minkowski-Hlawka…
We survey several significant results on the Bohr inequality and presented its generalizations in some new approaches. These are some Bohr type inequalities of Hilbert space operators related to the matrix order and the Jensen inequality.…
We give a representation of the fractional integral for symmetric Markovian semigroups as the projection of martingale transforms and prove the Hardy-Littlewood-Sobolev(HLS) inequality based on this representation. The proof rests on a new…
We establish a new perturbation theory for orthogonal polynomials using a Riemann--Hilbert approach and consider applications in numerical linear algebra and random matrix theory. This new approach shows that the orthogonal polynomials with…
In this paper we establish a refinement of the companion of Ostrowski inequality for functions of bounded variation. Applications for the trapezoid inequality, the mid-point inequality, and to probability density functions are also given.
The development of high-degree interpolation polynomials which use the values of the function and its subsequent derivatives is reformulated. Also, we present a variant of new formula in barycentric form.
We prove an invariant Harnack's inequality for operators in non-divergence form structured on Heisenberg vector fields when the coefficient matrix is uniformly positive definite, continuous, and symplectic. The method consists in…
Considering Wirtinger's inequality for piece-wise equipartite functions we find a discrete version of this classical inequality. The main tool we use is the theorem of classification of isometries. Our approach provides a new elementary…