A singular operator with Cauchy kernel on the subspaces of weight Lebesgue space is considered. A sufficient condition for a bounded action of this operator from a subspace to another subspace of weight Lebesgue space of functions is found. These conditions are not identical withMuckenhoupt conditions. Moreover, the completeness, minimality, and basicity of sines and cosines systems are conside...

Neutral community models have shown that limited migration can have a pervasive influence on the taxonomic composition of local communities even when all individuals are assumed of equivalent ecological fitness. Notably, the spatially implicit neutral theory yields a single parameter I for the immigration-drift equilibrium in a local community. In the case of plants, seed dispersal is considere...

We derive asymptotic normality of kernel type deconvolution density estimators. In particular we consider deconvolution problems where the known component of the convolution has a symmetric λ-stable distribution, 0 < λ ≤ 2. It turns out that the limit behavior changes if the exponent parameter λ passes the value one, the case of Cauchy deconvolution. AMS classification: primary 62G05; secondary...

We treat the Cauchy problem for nonlinear system of viscoelasticity with memory term. We study the existence and time decay of the solution to this nonlinear problem. The kernel of the memory term includes integrable singularity at zero and polynomial decay at infinity. We prove the existence of a global solution for space dimensions n ≥ 3 and arbitrary quadratic nonlinearities.

In this paper we propose the iterated projection method for the approximate solution of an integro-differential equations with Cauchy kernel in L2([−1, 1],C) using Legendre polynomials. We prove the convergence of the method. A system of linear equations is to be solved. Numerical examples illustrate the theoretical results. AMS Mathematics Subject Classification : 45E05, 35J15.

A singular Cauchy-Nicoletti problem for a system of three ordinary differential equations is considered. An approach which combines topological method of T. Ważewski and Schauder’s principle is used. Theorem concerning the existence of a solution of this problem (a graph of which lies in a given domain) is proved. Moreover, an estimation of its coordinates is obtained.

We establish the existence of solutions to Cauchy problem for a large class nonlinear parabolic equations including fractional semilinear equations, higher-order and viscous Hamilton–Jacobi by using majorant kernel introduced in Ishige et al. (2020).

Support vector machines (SVMs) belong to the class of modern statistical machine learning techniques and can be described as M-estimators with a Hilbert norm regularization term for functions. SVMs are consistent and robust for classification and regression purposes if based on a Lipschitz continuous loss and a bounded continuous kernel with a dense reproducing kernel Hilbert space. For regress...

Based on the theory of Dunkl operators, this paper presents a general concept of multivariable Hermite polynomials and Hermite functions which are associated with finite reflection groups on R . The definition and properties of these generalized Hermite systems extend naturally those of their classical counterparts; partial derivatives and the usual exponential kernel are here replaced by Dunkl...

Kernel sparse coding is an effective strategy to capture the non-linear structure of data samples. However, how to learn a robust kernel dictionary remains an open problem. In this paper, we propose a new optimization model to learn the robust kernel dictionary while isolating outliers in the training samples. This model is essentially based on the decomposition of the reconstruction error into...