6 papers
The Four-Point Picard Theorem for Quaternionic Slice Regular Functions
Guangbin Ren, Xin Zhao
An entire slice regular function can omit four prescribed quaternionic values only in the affine-dependent case. More precisely, four affinely independent…
Monogenic functions over real alternative *-algebras: fundamental results and applications
Qinghai Huo, Guangbin Ren, Zhenghua Xu
The concept of monogenic functions over real alternative -algebras has recently been introduced to unify several classical monogenic (or regular) functions theories in hyperc…
Slice Fueter-regular functions on arbitrary domains in octonions
Xinyuan Dou, Guangbin Ren, Zeping Zhu +1
This paper is concerned with a class of generalized slice Fueter-regular functions on arbitrary domains in O with local stem functions. Some classical theorems such as the maximum…
Octonionic isometric isomorphisms and partial isometry
Qinghai Huo, Guangbin Ren, Zhenghua Xu
Very recently, two new notions of para-linear mappings and weak associative orthonormal bases were introduced in octonionic functional analysis, which have been proved to be powerf…
Octonionic Riesz-Dunford functional calculus
Qinghai Huo, Guangbin Ren, Irene Sabadini +1
The Riesz-Dunford functional calculus over the algebra of octonions, denoted by , has long been an open problem due to the nonassociativity of octonions. Two core obsta…
Octonionic Para-linear Self-Adjoint Operators and Spectral Decomposition
Qinghai Huo, Guangbin Ren, Irene Sabadini
This paper presents a groundbreaking advancement in the theory of operators defined on octonionic Hilbert spaces, successfully resolving a fundamental challenge that has persisted…