Related papers: Multiplicative isometries on the Smirnov class
A fully implementable filtered polynomial approximation on spherical shells is considered. The method proposed is a quadrature-based version of a filtered polynomial approximation. The radial direction and the angular direction of the…
We discuss several classical and recent proofs of the isoperimetric inequality and the Sobolev inequality.
In this paper, we investigate the differential smoothness of skew PBW extensions over commutative polynomial rings on one and two indeterminates.
In a compact orbifold, for small prescribed volume, an isoperimetric region is close to a small metric ball; in a Euclidean orbifold, it is a small metric ball.
The article proves an assertion analogous to the Littlewood-Paley theorem for the orthoprojectors onto mutually orthogonal subspaces of piecewise polynomial functions on the cube $ I^d. $ This assertion provides an upper estimate for the…
We study a generalization of the classical correspondence between homogeneous quadratic polynomials, quadratic forms, and symmetric/alternating bilinear forms to forms in $n$ variables. The main tool is combinatorial polarization, and the…
Sarnak obtained the asymptotic formula of the sum of the class numbers of indefinite binary quadratic forms from the prime geodesic theorem for the modular group. In the present paper, we show several asymptotic formulas of partial sums of…
Classes of simple polynomial and simple trigonometric splines given by Fourier series are considered. It is shown that the class of simple trigonometric splines includes the class of simple polynomial splines. For some parameter values, the…
A version of Markov's estimate for the derivative of a polynomial is proved with the interval [-1,1] replaced by an arbitrary continuum in the complex plane.
We study flexible polyhedral nets in isotropic geometry. This geometry has a degenerate metric, but there is a natural notion of flexibility. We study infinitesimal and finite flexibility, and classify all finitely flexible polyhedral nets…
Various applications of the multiple scattering technique to calculating Casimir energy are described. These include the interaction between dilute bodies of various sizes and shapes, temperature dependence, interactions with multilayered…
The problem of interpolation at $(n+1)^2$ points on the unit sphere $\mathbb{S}^2$ by spherical polynomials of degree at most $n$ is proved to have a unique solution for several sets of points. The points are located on a number of circles…
The moduli space of degree $d$ morphisms on $\mathbb{P}^1$ has received much study. McMullen showed that, except for certain families of Latt\`es maps, there is a finite-to-one correspondence (over $\mathbb{C}$) between classes of morphisms…
We review known results concerning powers and products of $(m,p)$-isometries with a view to providing elementary proofs based on properties of polynomials. We consider also the situation when $p=\infty$ where we find elements of graph…
We introduce a general class of symmetric polynomials that have saturated Newton polytope and their Newton polytope has integer decomposition property. The class covers numerous previously studied symmetric polynomials.
A new class of structured matrices is presented and a closed form formula for their determinant is established. This formula has strong connections with the one for Vandermonde matrices.
The purpose of this thesis is to study classical combinatorial objects, such as polytopes, polytopal complexes, and subspace arrangements, using tools that have been developed in combinatorial topology, especially those tools developed in…
We obtain, in local coordinates, the explicit form of the two-dimensional, super-integrable systems of Matveev and Shevchishin involving cubic integrals. This enables us to determine for which values of the parameters these systems are…
We study characteristic polynomials of symmetric matrices with entries ${i+j\choose i}$ the binomial coefficients, over finite fields.
We investigate the isomorphism types of combinatorial geometries arising from Hrushovski's flat strongly minimal structures and answer some questions from Hrushovski's original paper.