Related papers: New variational arguments regarding the Blaschke-L…

In the presence of a positive, compactly supported measure on an affine algebraic curve, we relate the density of polynomials in Lebesgue $L^2$-space to the existence of analytic bounded point evaluations. Analogues to the complex plane…

We show that product Chebyshev polynomial meshes can be used, in a fully discrete way, to evaluate with rigorous error bounds the Lebesgue constant, i.e. the maximum of the Lebesgue function, for a class of polynomial projectors on cube,…

In this note some structural properties of grand variable exponent Lebesgue/ Morrey spaces over spaces of homogeneous type are obtained. In particular, it is proved that the closure of the class of bounded functions and the closure of…

We deduce mixed quasi-norm estimates of Lebesgue types on semi-continuous convolutions between sequences and functions which may be periodic or possess a weaker form of periodicity in certain directions. In these directions, the Lebesgue…

We recall first the relations between the syzygies of the Jacobian ideal of the defining equation for a projective hypersurface $V$ with isolated singularities and the versality properties of $V$, as studied by du Plessis and Wall. Then we…

This paper is concerned with the Cauchy-Dirichlet problem for a doubly nonlinear parabolic equation involving variable exponents and provides some theorems on existence and regularity of strong solutions. In the proof of these results, we…

In this paper, we establish asymptotic formulae with optimal errors for the number of rational points that are close to a planar curve, which unify and extend the results of Beresnevich-Dickinson-Velani and Vaughan-Velani. Furthermore, we…

We consider the possibility to use the areas of two-simplexes, instead of lengths of edges, as the dynamical variables of Regge calculus. We show that if the action of Regge calculus is varied with respect to the areas of two-simplexes, and…

This paper studies the existence of invariant smooth Lagrangian graphs for Tonelli Hamiltonian systems with symmetries. In particular, we consider Tonelli Hamiltonians with n independent but not necessarily involutive constants of motion…

We prove that among all constant width bodies of revolution, the minimum of the ratio of the volume to the cubed width is attained by the constant width body obtained by rotation of the Reuleaux triangle about an axis of symmetry.

Several sums of Neumann series with Bessel and trigonometric functions are evaluated, as finite sums of trigonometric functions. They arise from a generalization of the Neumann expansion of the eigenstates of the Laplacian in regular…

We prove a duality theorem the computation of certain Bellman functions is usually based on. As a byproduct, we obtain sharp results about the norms of monotonic rearrangements. The main novelty of our approach is a special class of…

We develop contractive finite dimensional realizations for rational matrix functions of one variable on domains that are not simply connected, such as the annulus. The proof uses multivariable contractive realization results as well as…

In continuation of the paper [3], we discuss various consequences of Hahn-Banach theorem for bounded b-linear functional in linear n-normed space and describe the notion of reflexivity of linear n-normed space with respect to bounded…

In this paper we introduce two new notions of sectional curvature for Riemannian manifolds with density. Under both notions of curvature we classify the constant curvature manifolds. We also prove generalizations of the theorems of…

Variational calculus on a vector bundle E equipped with a structure of a general algebroid is developed, together with the corresponding analogs of Euler-Lagrange equations. Constrained systems are introduced in the variational and in the…

This paper is concerned with complex Banach-space valued functions of the form $$ \hat{f}_k(r\cos\theta,r\sin\theta,z)=\mathrm{e}^{\mathrm{i} k \theta}f_k(r,z), \qquad r \in [0,\infty), \theta \in \mathbb{T}^1, z \in \mathbb{R}, $$ for some…

We study differential operators associated with families of polynomials orthonormal with respect to certain measures. These operators, when applied to the Fourier transforms of such measures, produce basis functions for expansions of…

The Euler-Gauss linear transformation formula for the hypergeometric function was extended by Goursat for the case of logarithmic singularities. By replacing the perturbed Bessel differential equation by a monodromic functional equation,…

Invariant Lagrangians yield invariant Euler-Lagrange equations, and it was discussed in the literature how to compute those using various local methods. The focus of this paper is on global algebraic differential invariants. In this case…