相关论文: The decay of the Walsh coefficients of smooth func…

We establish formulas for the $b$-adic Walsh coefficients of functions in $C^\alpha[0,1]$ for an integer $\alpha \geq 1$ and give upper bounds on the Walsh coefficients of these functions. We also study the Walsh coefficients of periodic…

For convex univalent functions we give instances where the sharp bound for various coefficient functionals are identical to those for the corresponding bound for the inverse function. We give instances where the sharp bounds differ and also…

We suggest an upper bound on binomial coefficients that holds over the entire parameter range and whose form repeats the form of the de Moivre-Laplace approximation of the symmetric binomial distribution. Using the bound, we estimate the…

Fractional derivatives are a well-studied generalization of integer order derivatives. Naturally, for optimization, it is of interest to understand the convergence properties of gradient descent using fractional derivatives. Convergence…

We consider the behaviour of holomorphic functions on a bounded open subset of the plane, satisfying a Lipschitz condition with exponent $\alpha$, with $0<\alpha<1$, in the vicinity of an exceptional boundary point where all such functions…

We demonstrate that shearlet systems yield superior $N$-term approximation rates compared with wavelet systems of functions whose first or higher order derivatives are smooth away from smooth discontinuity curves. We will also provide an…

We provide improved error bounds for kernel-based numerical differentiation in terms of growth functions when kernels are of a finite smoothness, such as polyharmonic splines, thin plate splines or Wendland kernels. In contrast to existing…

We study multivariate integration and approximation for functions belonging to a weighted reproducing kernel Hilbert space based on half-period cosine functions in the worst-case setting. The weights in the norm of the function space depend…

We characterize the polynomial decay of orbits of Hilbert space $C_0$-semigroups in resolvent terms. We also show that results of the same type for general Banach space semigroups and functions obtained recently in the paper by C.J.K.Batty…

We prove that any given function can be smoothly approximated by functions lying in the kernel of a linear operator involving at least one fractional component. The setting in which we work is very general, since it takes into account…

We consider nonparametric regression with functional covariates, that is, they are elements of an infinite-dimensional Hilbert space. A locally polynomial estimator is constructed, where an orthonormal basis and various tuning parameters…

We obtain the decay bounds for Chebyshev series coefficients of functions with finite Vitali variation on the unit square. A generalization of the well known identity, which relates exact and approximated coefficients, obtained using the…

We prove that for a large class of multiplicative functions, referred to as generalized divisor functions, it is possible to find a lower bound for the corresponding variance in arithmetic progressions. As a main corollary, we deduce such a…

We prove a new upper bound for the number of smooth values of a polynomial with integer coefficients. This improves Timofeev's previous result unless the polynomial is a product of linear polynomials with integer coefficients. As an…

We prove lower bounds on the complexity of finding $\epsilon$-stationary points (points $x$ such that $\|\nabla f(x)\| \le \epsilon$) of smooth, high-dimensional, and potentially non-convex functions $f$. We consider oracle-based complexity…

In this paper it is shown that higher order quasiconvex functions suitable in the variational treatment of problems involving second derivatives may be extended to the space of all matrices as classical quasiconvex functions. Precisely, it…

We propose inferential tools for functional linear quantile regression where the conditional quantile of a scalar response is assumed to be a linear functional of a functional covariate. In contrast to conventional approaches, we employ…

This is a first version of a paper concerning abstract evolution equation with fractional time derivatives. Maximal regularity results in spaces of continuous and Hoelder continuous functions are described.

In this paper we compute the Hilbert functions of irreducible (or smooth) and reduced arithmetically Gorenstein schemes that are twisted anti-canonical divisors on arithmetically Cohen-Macaulay schemes. We also prove some folklore results…

A distributed order fractional diffusion equation is considered. Distributed order derivatives are fractional derivatives that have been integrated over the order of the derivative within a given range. In this paper sub-diffusive cases are…