Related papers: Continuous slice functional calculus in quaternion…

The Fueter-Sce-Qian mapping theorem is a two steps procedure to extend holomorphic functions of one complex variable to quaternionic or Clifford algebra-valued functions in the kernel of a suitable generalized Cauchy-Riemann operator. Using…

We consider a quaternionic analogue of the univariate complex Hermite polynomials and study some of their analytic properties in some detail. We obtain their integral representation as well as the operational formulas of exponential and…

We prove a Cauchy-type integral formula for slice-regular functions where the integration is performed on the boundary of an open subset of the quaternionic space, with no requirement of axial symmetry. In particular, we get a local…

We investigate the new definition of analytic functional calculus in the terms of representation theory of SL2(R). We avoid any usage of its algebraic homomorphism property and replace it by the demand to be an intertwining operator. The…

The Fueter-Sce mapping theorem stands as one of the most profound outcomes in complex and hypercomplex analysis, producing hypercomplex generalizations of holomorphic functions. In recent years, delving into the factorization of the second…

Holomorphic Cliffordian functions of order $k$ are functions in the kernel of the differential operator $\overline{\partial}\Delta^k$. When $\overline{\partial}\Delta^k$ is applied to functions defined on the paravector space of some…

The aim of this paper is to give an overview of the spectral theories associated with the notions of holomorphicity in dimension greater than one. A first natural extension is the theory of several complex variables whose Cauchy formula is…

In this paper we investigate some basic results on the slice regular Besov spaces of hyperholomorphic functions on the unit ball $\mathbb{B}.$ We also characterize the boundedness, compactness and find the essential norm estimates of…

The theory of slice regular functions over the quaternions, introduced by Gentili and Struppa in [5], was born on domains that intersect the real axis. This hypothesis can be overcome using the theory of stem functions introduced by Ghiloni…

This work studies slice functions over finite-dimensional division algebras. Their zero sets are studied in detail along with their multiplicative inverses, for which some unexpected phenomena are discovered. The results are applied to…

The decompositions of an element of a finite von Neumann algebra into the sum of a normal operator plus an s.o.t.-quasinilpotent operator, obtained using the Haagerup--Schultz hyperinvariant projections, behave well with respect to…

Area integral functions are introduced for sectorial operators on Hilbert spaces. We establish the equivalence relationship between the square and area integral functions. This immediately extends McIntosh/Yagi's results on $H^{\8}$…

We study universal approximation of continuous functionals on compact subsets of products of Hilbert spaces. We prove that any such functional can be uniformly approximated by models that first take finitely many continuous linear…

This paper studies the singularities of Cullen-regular functions of one quaternionic variable. The quaternionic Laurent series prove to be Cullen-regular. The singularities of Cullen-regular functions are thus classified as removable,…

In this paper, we first prove that the S-spectrum of a bounded right quaternionic linear operator on a two-sided quaternionic Banach space is a union of the spectrum of some bounded linear operators on a complex Banach space. Furthermore,…

This paper aims to explore the concept of continuous \( K \)-frames in quaternionic Hilbert spaces. First, we investigate \( K \)-frames in a single quaternionic Hilbert space \( \mathcal{H} \), where \( K \) is a right $\mathbb{H}$-linear…

We develop a version of Herbrand's theorem for continuous logic and use it to prove that definable functions in infinite-dimensional Hilbert spaces are piecewise approximable by affine functions. We obtain similar results for definable…

In this paper we prove the spectral theorem for quaternionic unbounded normal operators using the notion of $S$-spectrum. The proof technique consists of first establishing a spectral theorem for quaternionic bounded normal operators and…

In this paper we prove a strong version of the Hilbert Nullstellensatz in the ring $\mathbb H[q_1,\ldots,q_n]$ of slice regular polynomials in several quaternionic variables. Our proof deeply depends on a detailed analysis of the common…

For a bounded quaternionic operator $T$ on a right quaternionic Hilbert space $\mathcal{H}$ and $\varepsilon >0$, the pseudo $S$-spectrum of $T$ is defined as \begin{align*} \Lambda_{\varepsilon}^{S}(T) := \sigma_S (T) \bigcup \left \{ q…