Classical operator theory in Banach and Hilbert spaces has been stimulated by several
problems in mathematics and physics. Moreover, the theory of holomorphic functions plays a …

This work inserts in the very fruitful study of quaternionic linear operators. This study is a
generalization of the complex case, but the noncommutative setting of quaternions shows …

In this paper we define a new function theory of slice monogenic functions of a Clifford
variable using the $ S $-functional calculus for Clifford numbers. Previous attempts of such a …

The theory of quaternionic operators has applications in several different fields, such as
quantum mechanics, fractional evolution problems, and quaternionic Schur analysis, just to …

In this paper we introduce fractional powers of quaternionic operators. Their definition is
based on the theory of slice hyperholomorphic functions and on the $ S $-resolvent …

Operator Theory on One-Sided Quaternion Linear Spaces: Intrinsic 𝑆-Functional Calculus and
Spectral Operators Page 1 Number 1297 Operator Theory on One-Sided Quaternion Linear …

In this paper we show how the spectral theory based on the notion of S-spectrum allows us
to study new classes of fractional diffusion and of fractional evolution processes. We prove …

In the recent years, there has been a lot of interest in fractional diffusion and fractional
evolution problems. The spectral theory on the S‐spectrum turned out to be an important tool …

Recently the S-spectrum approach to fractional diffusion problems has been applied to
vector operators with homogeneous Dirichlet boundary conditions. This method allows to …

The aim of this paper is to introduce the H1-functional calculus for harmonic functions over
the quaternions. More precisely, we give meanring to Df. T/for unbounded sectorial …