Related papers: Higher Order Approximation of Functions by Modifie…

In this paper we characterize the approximation schemes that satisfy Shapiro's theorem and we use this result for several classical approximation processes. In particular, we study approximation of operators by finite rank operators and…

In a strengthening of the G-Signature Theorem of Atiyah and Singer, we compute, at least in principle (modulo certain torsion of exponent dividing a power of the order of G), the class in equivariant K-homology of the signature operator on…

Submodularity is one of the most important properties in combinatorial optimization, and $k$-submodularity is a generalization of submodularity. Maximization of a $k$-submodular function requires an exponential number of value oracle…

An approach which unifies the Double Logarithmic Approximation at small x and the leading order DGLAP evolution of fragmentation functions at large x is presented. This approach reproduces exactly the Modified Leading Logarithm…

We consider a framework for the construction of iterative schemes for operator equations that combine low-rank approximation in tensor formats and adaptive approximation in a basis. Under fairly general assumptions, we obtain a rigorous…

A variational method is discussed, extending the Gaussian effective potential to higher orders. The single variational parameter is replaced by trial unknown two-point functions, with infinite variational parameters to be optimized by the…

This paper deals with a certain class of second-order conformally invariant operators acting on functions taking values in particular (finite-dimensional) irreducible representations of the orthogonal group. These operators can be seen as a…

A new notion of metric differentiability of set-valued functions at a point is introduced in terms of right and left limits of special set-valued metric divided differences of first order. A local metric linear approximant of a metrically…

In this paper we combine two existing approaches for approximating attractors. One of them approximates the attractors arbitrarily well by sublevel sets related to solutions of infinite dimensional linear programming problems. A downside…

In recent years, higher-order trace formulas of operator functions have attracted considerable attention to a large part of the perturbation theory community. In this direction, we prove estimates for traces of higher-order derivatives of…

It is known for linear operators with polynomial coefficients annihilating a given D-finite function that there is a trade-off between order and degree. Raising the order may give room for lowering the degree. The relationship between order…

In this note, we consider the complexity of optimizing a highly smooth (Lipschitz $k$-th order derivative) and strongly convex function, via calls to a $k$-th order oracle which returns the value and first $k$ derivatives of the function at…

The main objective of present investigation to obtain some Minkowski-type fractional integral inequalities using generalised proportional Hadamard fractional integral operators which is introduced by Rahman et al in the paper (certain…

An outstanding challenge in nonlinear systems theory is identification or learning of a given nonlinear system's Koopman operator directly from data or models. Advances in extended dynamic mode decomposition approaches and machine learning…

In the present note, we give the generalization of $\alpha-$Baskakov Durrmeyer operators depending on a real parameter $\rho$ > 0. We present the approximation results in Korovkin and weighted Korovkin spaces. We also prove the order of…

In this paper we consider the problem of the existence of higher derivatives of the function $t\mapsto\f(A+tK)$, where $\f$ is a function on the real line, $A$ is a self-adjoint operator, and $K$ is a bounded self-adjoint operator. We…

The problem of supervised classification (or discrimination) with functional data is considered, with a special interest on the popular k-nearest neighbors (k-NN) classifier. First, relying on a recent result by Cerou and Guyader (2006), we…

We give a negative answer to the Newman--Shapiro problem on weighted approximation for entire functions formulated in 1966 and motivated by the theory of operators on the Fock space. There exists a function in the Fock space such that its…

This paper studies a particular class of higher order conformally invariant dif- ferential operators and related integral operators acting on functions taking values in particular finite dimensional irreducible representations of the Spin…

Quadratic-support functions [Aravkin, Burke, and Pillonetto; J. Mach. Learn. Res. 14(1), 2013] constitute a parametric family of convex functions that includes a range of useful regularization terms found in applications of convex…