相关论文: The Optimal Dyadic Derivative

Scientific studies often require the precise calculation of derivatives. In many cases an analytical calculation is not feasible and one resorts to evaluating derivatives numerically. These are error-prone, especially for higher-order…

Given a variety $Y$ with a rectangular Lefschetz decomposition of its derived category, we consider a degree $n$ cyclic cover $X \to Y$ ramified over a divisor $Z \subset Y$. We construct semiorthogonal decompositions of $\mathrm{D^b}(X)$…

Let $G$ be a compact connected Lie group with a maximal torus $T$. Let $A$, $B$ be $G$-$\mathrm{C}^\ast$-algebras. We define certain divided difference operators on Kasparov's $T$-equivariant $KK$-group $KK_T(A,B)$ and show that $KK_G(A,B)$…

How to find "best rational approximations" of maximal commutative subgroups of GL(n,R)? In this paper we pose and make first steps in the study of this problem. It contains both classical problems of Diophantine and simultaneous…

The dyadic representation of any singular integral operator, as an average of dyadic model operators, has found many applications. While for many purposes it is enough to have such a representation for a "suitable class" of test functions,…

We obtain similar types of conclusions as that of Br\"{u}ck [1] for two differential polynomials which in turn radically improve and generalize several existing results. Moreover, a number of examples have been exhibited to justify the…

We consider the discrete analogue of a fractional integral operator on the Heisenberg group, for which we are able to prove nearly sharp results by means of a simple argument of a combinatorial nature.

The idea behind Poisson approximation to the binomial distribution was used in [J. de la Cal, F. Luquin, J. Approx. Theory, 68(3), 1992, 322-329] and subsequent papers in order to establish the convergence of suitable sequences of positive…

We approximate the spectra of a class of $2n$-order differential operators using isogeometric analysis in mixed formulations. This class includes a wide range of differential operators such as those arising in elliptic, biharmonic,…

We define a class of discrete operators that, in particular, include the delta and nabla fractional operators.

The purpose of this paper is to generalize the regular Optimal Reduction Theorem to general proper Dirac actions, formulated both in terms of point and orbit reduction. A comparison to general standard singular Dirac reduction is given…

We prove the Euler-Lagrange delta-differential equations for problems of the calculus of variations on arbitrary time scales with delta-integral functionals depending on higher-order delta derivatives.

We give a characterization of optimal transport plans for a variant of the usual quadratic transport cost introduced in [33]. Optimal plans are composition of a deterministic transport given by the gradient of a continuously differentiable…

We construct a set $M_d$ whose points parametrize families of Meixner polynomials in $d$ variables. There is a natural bispectral involution $b$ on $M_d$ which corresponds to a symmetry between the variables and the degree indices of the…

We introduce a suitable notion of integral operators (comprising the fractional Laplacian as a particular case) acting on functions with minimal requirements at infinity. For these functions, the classical definition would lead to divergent…

In this article we give an order-dividing bijective function between cyclic and non cyclic groups of finite order. In particular, we prove that there exists a bijective function from D_{2n} to Z_{2n} for any natural integer n; and from Z_p…

In this paper we partially settle our conjecture from [1] (math.SP/0701143) on roots of eigenpolynomials for degenerate exactly-solvable operators. Namely, for any such operator, we establish a lower bound (which supports our conjecture)…

Using Dunkl operators, we introduce a continuous family of canonical invariants of finite reflection groups. We verify that the elementary canonical invariants of the symmetric group are deformations of the elementary symmetric polynomials.…

Explicit inversion formulas for a subclass of integral operators with $D$-difference kernels on a finite interval are obtained. A case of the positive operators is treated in greater detail. An application to the inverse problem to recover…

We consider differential operators defined as Friedrichs extensions of quadratic forms with non-smooth coefficients. We prove a two term optimal asymptotic for the Riesz means of these operators and thereby also reprove an optimal Weyl law…