Related papers: Weighted Sonine conditions and application

This work is motivated by the frequent occurrence of boundary value problems with various boundary conditions in the modeling of some problems in engineering and physical science. Here we propose a new technique to force the positive…

The paper introduces new sufficient conditions of strict positive definiteness for kernels on d-dimensional spheres which are not radially symmetric but possess specific coefficient structures. The results use the series expansion of the…

Using the log-convexity of the Gamma function and Euler's reflection formula, we give a new proof of a classical weighted sine product inequality. Two different parameter choices yield two competing upper bounds for the same product. We…

In this paper, we study the weighted composition operator on the Fock space $\mf$ of slice regular functions. First, we characterize the boundedness and compactness of the weighted composition operator. Subsequently, we describe all the…

In this paper we introduce and investigate a new kind of functional (including ordinary and evolutionary partial) differential equations. The main goal of this paper is to explore our new philosophy by some examples on functional ODEs and…

This paper provides a nonparametric analysis for several classes of models, with cases such as classical measurement error, regression with errors in variables, factor models and other models that may be represented in a form involving…

Learning equivariant representations is a promising way to reduce sample and model complexity and improve the generalization performance of deep neural networks. The spherical CNNs are successful examples, producing SO(3)-equivariant…

Derived from the results in [Giang et al.: \emph{Convolutions for the Fourier transforms with geometric variables and applications}, Math. Nachr. 283(12) (2010), 1758--1770], in this paper, we devoted to studying the boundedness properties…

The spectral analysis of operators in heterogeneous and aging media typically requires a functional framework that extends beyond the standard Hilbertian setting. In this paper, we establish a rigorous distributional theory for a class of…

In this paper, using some aspects of convex functions, we refine discrete Jensen's inequality via weight functions. Then, using these results, we give some applications in different abstract spaces and obtain some new interesting…

Smoothed analysis of complexity bounds and condition numbers has been done, so far, on a case by case basis. In this paper we consider a reasonably large class of condition numbers for problems over the complex numbers and we obtain…

The constraint nondegeneracy condition is one of the most relevant and useful constraint qualifications in nonlinear semidefinite programming. It can be characterized in terms of any fixed orthonormal basis of the, let us say,…

The present paper is devoted to studying of some weighted H\"older spaces. These spaces are designed in the way to serve as a framework for studying different statements for the thin film equations in weighted classes of smooth functions in…

Conditional generative adversarial networks (cGANs) have been widely researched to generate class conditional images using a single generator. However, in the conventional cGANs techniques, it is still challenging for the generator to learn…

This paper studies a class of linear parabolic equations with measurable coefficients in divergence form whose volumetric heat capacity coefficients are assumed to be in some Muckenhoupt class of weights. As such, the coefficients can be…

We show how the sine and cosine integrals may be usefully employed in the evaluation of some more complex integrals.

Integral equations for the spin-weighted spheroidal wave functions is given. For the prolate spheroidal wave function with m=0, there exists the integral equation whose kernel is(sin x)/x, and the sinc function kernel (sin x)/x is of great…

We consider orthogonal polynomials on the unit circle associated with certain semi-classical weight functions. This means that the Pearson-type differential equations satisfied by these weight functions involve two polynomials of degree at…

In this paper, we study the existence of positive solutions for nonlinear fractional differential equations with a singular weight. We derive Green's function and corresponding integral operator and then examine the compactness of the…

Some results about existence, uniqueness, and attractive behaviour of solutions for nonlinear Volterra integral equations with non-convolution kernels are presented in this paper. These results are based on similar ones about nonlinear…