Recent results in geometry processing have shown that shape segmentation, comparison, and analysis can be successfully addressed through the heat diffusion kernel. In this paper, we focus our attention on the properties (e.g., scale-invariance, semi-group property, robustness to noise) of the wFEM heat kernel, recently proposed in [PF10], and its application to shape comparison and feature-driv...

This paper is devoted to the study of reproducing kernel Hilbert spaces. We focus on multipliers of reproducing kernel Banach and Hilbert spaces. In particular, we try to extend this concept and prove some related theorems. Moreover, we focus on reproducing kernels in vector-valued reproducing kernel Hilbert spaces. In particular, we extend reproducing kernels to relative reproducing kernels an...

This paper considers the regularized learning algorithm associated with the leastsquare loss and reproducing kernel Hilbert spaces. The target is the error analysis for the regression problem in learning theory. A novel regularization approach is presented, which yields satisfactory learning rates. The rates depend on the approximation property and the capacity of the reproducing kernel Hilbert...

In this paper we develop a Sz.-Nagy-Foiaş type theory of characteristic functions and functional models on noncommutative domains varieties in $$B(\mathcal{H})^n$$ , where $$B(\mathcal{H})$$ is the algebra all bounded linear operators Hilbert space $$\mathcal{H}$$ associated with admissible free holomorphic for operator model theory. This includes, particular, large class commutative . case, ar...

For some general linear integral operator equations, we investigate consequent initial value problems by using the theory of reproducing kernels. A new method is proposed which – in particular – generates a new field among initial value problems, linear integral operators, eigenfunctions and values, integral transforms and reproducing kernels. In particular, examples are worked out for the inte...

A simple method for solving Prandtl's integro-differential equation is proposed based on a new reproducing kernel space. Using a transformation and modifying the traditional reproducing kernel method, the singular term is removed and the analytical representation of the exact solution is obtained in the form of series in the new reproducing kernel space. Compared with known investigations, its ...

The paper concerns the design of nonparametric low-pass filters that have the property of reproducing a polynomial of a given degree. Two approaches are considered. The first is locally weighted polynomial regression (LWPR), which leads to linear filters depending on three parameters: the bandwidth, the order of the fitting polynomial, and the kernel. We find a remarkable linear (hyperbolic) re...