Related papers: Weighted Sonine conditions and application
We propose the introduction of nonlinear operation into the feature generation process in convolutional neural networks. This nonlinearity can be implemented in various ways. First we discuss the use of nonlinearities in the process of data…
This paper discusses the solution of nonlinear integral equations with noisy integral kernels as they appear in nonparametric instrumental regression. We propose a regularized Newton-type iteration and establish convergence and convergence…
In this article we consider certain types of weighted generalized functions associated with nondegenerate quadratic forms. Such functions and their derivatives are used for constructing fundamental solutions of iterated ultra-hyperbolic…
In this paper, we introduce the general fractional integrals and derivatives of arbitrary order and study some of their basic properties and particular cases. First, a suitable generalization of the Sonine condition is presented and some…
We consider functional linear regression models where functional outcomes are associated with scalar predictors by coefficient functions with shape constraints, such as monotonicity and convexity, that apply to sub-domains of interest. To…
We associate a weight function to pairs consisting of a smooth and proper variety X over a complete discretely valued field and a differential form on X of maximal degree. This weight function is a real-valued function on the…
The existence and uniqueness of solution to a one-dimensional hyperbolic integro-differential problem arising in viscoelasticity is here considered. The kernel, in the linear viscoelasticity equation, represents the relaxation function…
Due to its convolution nature, the Stieltjes integral equation can be diagonalized by Mellin transform. Several explicit resolvent kernels were obtained over the years, all of convolution type. The conditions on the given function under…
New necessary and sufficient conditions are given for the quantization of a class of periodic second order non-homogeneous ordinary differential equations in the complex plane in this paper. The problem is studied from the viewpoint of…
This article studies sufficient conditions on families of approximating kernels which provide $N$--term approximation errors from an associated nonlinear approximation space which match the best known orders of $N$--term wavelet expansion.…
The rapid and accurate evaluation of convolutions with singular kernels plays crucial roles in a wide range of scientific and engineering applications. Building on the recently introduced Truncated Fourier Filtering method for smooth…
In this paper we obtain new sufficient conditions for representation of a function as an absolutely convergent Fourier integral. Unlike those known earlier, these conditions are given in terms of belonging to weighted spaces. Adding weights…
We study stochastic partial differential equations of the reaction-diffusion type. We show that, even if the forcing is very degenerate (i.e. has not full rank), one has exponential convergence towards the invariant measure. The convergence…
We characterize the condition $(\Omega)$ for smooth kernels of partial differential operators in terms of the existence of shifted fundamental solutions satisfying certain properties. The conditions $(P\Omega)$ and…
A new method of composition orthogonality is introduced. It is applied to generate new sequences of orthogonal polynomials and functions. In particular, classical orthogonal polynomials are interpreted in the sense of composition…
Inspired by prior work of Bruinier and Ono and Mertens and Rolen, we study class polynomials for non-holomorphic modular functions arising from modular forms of negative weight. In particular, we give general conditions for the…
We study orthogonal polynomial ensembles whose weights are deformations of exponential weights, in the limit of a large number of particles. The deformation symbols we consider affect local fluctuations of the ensemble around a bulk point…
We demonstrate that a conditional wavefunction theory enables a unified and efficient treatment of the equilibrium structure and nonadiabatic dynamics of correlated electron-ion systems. The conditional decomposition of the many-body…
This article is devoted to the analysis of semilinear, parabolic, Stochastic Partial Differential Equations, with slow and fast time scales. Asymptotically, an averaging principle holds: the slow component converges to the solution of…
The covariant Poisson equation for Lie algebra-valued mappings defined in 3-dimensional Euclidean space is studied using functional analytic methods. Weighted covariant Sobolev spaces are defined and used to derive sufficient conditions for…