Generalized spherical mean value operators on Euclidean space

Generalized Euclidean distance matrices

Euclidean distance matrices (EDM) are symmetric nonnegative matrices with several interesting properties. In this article, we introduce a wider class of matrices called generalized Euclidean distance matrices (GDMs) that include EDMs. Each GDM is an entry-wise nonnegative matrix. A GDM is not symmetric unless it is an EDM. By some new techniques, we show that many significant results on Euclidean distance matrices can be extended to generalized Euclidean distance matrices. These contain results about eigenvalues, inverse, determinant, spectral radius, Moore-Penrose inverse and some majorizatio…

Generalized Euclidean Operator Radius

In this paper, we introduce the $f-$operator radius of Hilbert space operators as a generalization of the Euclidean operator radius and the $q-$operator radius. Properties of the newly defined radius are discussed, emphasizing how it extends some known results in the literature.

2元组算子的广义欧几里得算子半径不等式的改进

Refinements of generalized Euclidean operator radius inequalities of 2-tuple operators

该研究针对容许A-伴随的2元组算子的A-欧几里得算子半径推导若干上下界，证明其改进了已有相关界，并借此得到更精确的A-数值半径界。

Generalized subdifferentials of spectral functions over Euclidean Jordan algebras

This paper is devoted to the study of generalized subdifferentials of spectral functions over Euclidean Jordan algebras. Spectral functions appear often in optimization problems playing the role of "regularizer", "barrier", "penalty function" and many others. We provide formulae for the regular, approximate and horizon subdifferentials of spectral functions. In addition, under local lower semicontinuity, we also furnish a formula for the Clarke subdifferential, thus extending an earlier result by Baes. As application, we compute the generalized subdifferentials of the function that maps an ele…