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We study superharmonic functions for Schr\"odinger operators on general weighted graphs. Specifically, we prove two decompositions which both go under the name Riesz decomposition in the literature. The first one decomposes a superharmonic…

Analysis of PDEs · Mathematics 2022-04-13 Florian Fischer , Matthias Keller

We introduce a class of rings using which we define the concept of skew regularity for quaternion-valued functions over quaternions. It is shown that the notion of skew regularity coincides with the concept of slice regularity over…

Rings and Algebras · Mathematics 2022-11-15 Masood Aryapoor

We generalize the representation formula from slice-domains of regularity to general Riemann slice-domains. This result allows us to extend the $*$-product of slice regular functions on axially symmetric domains to certain Riemann…

Complex Variables · Mathematics 2018-09-26 Xinyuan Dou , Guangbin Ren

Inspired from the Cholewinski approach see [5], we investigate a family of Fock spaces in the quaternionic slice hyperholomorphic setting as well as some associated quaternionic linear operators. In a particular case, we reobtain the slice…

Complex Variables · Mathematics 2019-05-01 Kamal Diki

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…

Complex Variables · Mathematics 2025-05-13 Fabrizio Colombo , Antonino De Martino , Irene Sabadini

The theory of slice regular functions of a quaternionic variable extends the notion of holomorphic function to the quaternionic setting. This theory, already rich of results, is sometimes surprisingly different from the theory of…

Complex Variables · Mathematics 2014-04-14 Graziano Gentili , Giulia Sarfatti

In this paper we begin the study of Schur analysis and de Branges-Rovnyak spaces in the framework of Fueter hyperholomorphic functions. The difference with other approaches is that we consider the class of functions spanned by Appell-like…

Functional Analysis · Mathematics 2021-08-03 Daniel Alpay , Fabrizio Colombo , Kamal Diki , Irene Sabadini

In this paper we introduce the Schatten class of operators and the Berezin transform of operators in the quaternionic setting. The first topic is of great importance in operator theory but it is also necessary to study the second one…

Functional Analysis · Mathematics 2016-12-21 Fabrizio Colombo , Jonathan Gantner , Tim Janssens

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…

Complex Variables · Mathematics 2021-12-10 Fabrizio Colombo , Antonino De Martino , Irene Sabadini

The Fueter-Sce theorem is one of the most important results in hypercomplex analysis, providing a two-step procedure for constructing axially monogenic functions starting from holomorphic functions of one variable. In the first step, the…

Functional Analysis · Mathematics 2026-01-09 Antonino De Martino , Stefano Pinton

We construct a counterexample to a well-known extension theorem for slice regular functions, which motivates us to develop a theory of Riemann slice-domains by introducing a new topology on quaternions. By some paths describing axial…

Complex Variables · Mathematics 2019-02-13 Xinyuan Dou , Guangbin Ren

We continue investigating the superintegrability property of matrix models, i.e. factorization of the matrix model averages of characters. This paper focuses on the Gaussian Hermitian example, where the role of characters is played by the…

High Energy Physics - Theory · Physics 2023-01-26 A. Mironov , A. Morozov

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…

Operator Algebras · Mathematics 2013-10-10 Ken Dykema , Fedor Sukochev , Dmitriy Zanin

In this paper, we introduce the quaternionic slice polyanalytic functions and we prove some of their properties. Then, we apply the obtained results to begin the study of the quaternionic Fock and Bergman spaces in this new setting. In…

Complex Variables · Mathematics 2021-03-16 Daniel Alpay , Kamal Diki , Irene Sabadini

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,…

Functional Analysis · Mathematics 2020-05-21 El Hassan Benabdi , Mohamed Barraa

Harmonic and polyanalytic functional calculi have been recently defined for bounded commuting operators. Their definitions are based on the Cauchy formula of slice hyperholomorphic functions and on the factorization of the Laplace operator…

Spectral Theory · Mathematics 2023-04-21 Fabrizio Colombo , Antonino De Martino , Stefano Pinton

We study global properties of quaternionic slice regular functions (also called s-regular) defined on symmetric slice domains. In particular, thanks to new techniques and points of view, we can characterize the property of being one-slice…

Complex Variables · Mathematics 2019-01-03 Amedeo Altavilla , Chiara de Fabritiis

The main purpose of this paper is the study of a~new class of summing multilinear operators acting from the product of Banach lattices with some nontrivial lattice convexity. A~mixed Pietsch-Maurey-Rosenthal type factorization theorem for…

Functional Analysis · Mathematics 2017-06-20 Mieczysław Mastyło , Enrique A. Sánchez-Pérez

Reiner, Shaw and van Willigenburg showed that if two skew Schur functions s_A and s_B are equal, then the skew shapes A and B must have the same "row overlap partitions." Here we show that these row overlap equalities are also implied by a…

Combinatorics · Mathematics 2014-02-13 Peter R. W. McNamara

In this paper we summarize some known facts on slice topology in the quaternionic case, and we deepen some of them by proving new results and discussing some examples. We then show, following [18], how this setting allows us to generalize…

Complex Variables · Mathematics 2024-06-27 X. Dou , M. Jin , G. Ren , I. Sabadini