相关论文: Kernel and symbol criteria for Schatten classes an…

The universality properties of kernels characterize the class of functions that can be approximated in the associated reproducing kernel Hilbert space and are of fundamental importance in the theoretical underpinning of kernel methods in…

We describe the symbolic calculus of operators on the unit sphere in the complex n-space $\mathbb C^n$ defined by the Berezin quantization. In particular, we derive a explicit formula for the composition of Berezin symbol and with that a…

We provide a characterization for the continuous positive definite kernels on $\mathbb R^d$ that are invariant to linear isometries, i.e. invariant under the orthogonal group $O(d)$. Furthermore, we provide necessary and sufficient…

We study a new class of pseudo differential operators whose symbols satisfy the differential inequality with a mixture of homogeneities. On the other hand, by taking singular integral realization, it can be equivalently defined by kernels…

In this paper, we consider Hankel operators, with locally integrable symbols, densely defined on a family of Fock-type spaces whose weights are $C^3$-logarithmic growth functions with mild smoothness conditions. It is shown that a Hankel…

We characterize the Schatten class Toeplitz operators induced by a positive Borel measure on the unit disc and the reproducing kernel of the Bergman space $A^2_\omega$, where $\omega$ is a radial weight satisfying the doubling property…

Motivated by the study of kernels of bilinear pseudodifferential operators with symbols in a H\"ormander class of critical order, we investigate boundedness properties of strongly singular Calder\'on--Zygmund operators in the bilinear…

For a class of semilinear elliptic equations, we establish criteria that guarantee that the linearized operator associated with a solution satisfies certain spectral assumptions that are widely used in the analysis of the stability of…

We consider second-order partial differential operators $H$ in divergence form on $\Ri^d$ with a positive-semidefinite, symmetric, matrix $C$ of real $L_\infty$-coefficients and establish that $H$ is strongly elliptic if and only if the…

We establish continuity and Schatten-von Neumann properties for matrix operators with matrices satisfying mixed quasi-norm estimates. These considerations also include the case when the Lebesgue and Schatten parameters are allowed to stay…

The purpose of this paper is to study algebras of singular integral operators on $\mathbb{R}^{n}$ and nilpotent Lie groups that arise when one considers the composition of Calder\'on-Zygmund operators with different homogeneities, such as…

Strictly proper kernel scores are well-known tool in probabilistic forecasting, while characteristic kernels have been extensively investigated in the machine learning literature. We first show that both notions coincide, so that insights…

We study the learnability of a class of compact operators known as Schatten--von Neumann operators. These operators between infinite-dimensional function spaces play a central role in a variety of applications in learning theory and inverse…

By establishing some reproducing kernel estimates, we characterize the bounded, compact and Schatten $p$-class Toeplitz operators with positive measure symbols on the weighted Fock space $F^2_{\alpha,w}$ for $p\geq1$, where $w$ is a weight…

In this paper we give several global characterisations of the Hormander class of pseudo-differential operators on compact Lie groups. The result is applied to give criteria for the ellipticity and the global hypoellipticity of…

This work aims to develop a global quantization in the concrete settings of two graded nilpotent Lie groups of 3-step; namely of the Engel group and the Cartan group. We provide a preliminary analysis on the structure and the…

We consider singular integral operators and maximal singular integral operators with rough kernels on homogeneous groups. We prove certain estimates for the operators that imply $L^p$ boundedness of them by an extrapolation argument under a…

Given a manifold with boundary endowed with an action of a discrete group on it, we consider the algebra of operators generated by elements in the Boutet de Monvel algebra of pseudodifferential boundary value problems and shift operators…

We present in this work a new family of kernels to compare positive measures on arbitrary spaces $\Xcal$ endowed with a positive kernel $\kappa$, which translates naturally into kernels between histograms or clouds of points. We first cover…

This paper addresses the three following questions. (i) How the structures of group and of chain of groups enter nuclear, atomic and molecular spectroscopy? (ii) How these structures can be exploited, in a quantum- mechanical framework, in…