Related papers: Complex structures and slice-regular functions on …
This paper is devoted to the classification and studying properties of complex unital $3$-dimensional structurable algebras. We provide a complete list of non-isomorphic classes, identifying five algebras for type $(2, 1)$ and two algebras…
Subharmonic functions associated with the stationary Schrodinger operator are its weak subsolutions under appropriate assumptions on the potential of the operator. We prove for these functions analogs of several classical results on…
Holomorphic functions play a crucial role in operator theory and the Cauchy formula is a very important tool to define functions of operators. The Fueter-Sce-Qian extension theorem is a two steps procedure to extend holomorphic functions to…
By complexifying a Hamiltonian system one obtains dynamics on a holomorphic symplectic manifold. To invert this construction we present a theory of real forms which not only recovers the original system but also yields different real…
We introduce the notion of a chopped and sliced cone in combinatorial geometry and prove two structure theorems for the number of integral points in the individual slices of such a cone. We observe that this notion applies to weight…
In this article, we deal with the structure of the spherical Hall algebra of coherent sheaves with parabolic structures on a smooth projective curve of arbitrary genus. We provide a shuffle-like presentation of the vector bundle part and…
We investigate Grothendieck rings appearing in real geometry, notably for arc-symmetric sets, and focus on the relative case in analogy with the properties of the ring of algebraically constructible functions defined by McCrory and…
We describe an algorithm that associates to each positive real number $r$ and each finite collection $C_r$ of planar pixels of size $r$ a planar piecewise linear set $S_r$ with the following additional property: if $C_r$ is the collection…
Algebraically constructible functions connect real algebra with the topology of algebraic sets. In this survey we present some history, definitions, properties, and algebraic characterizations of algebraically constructible functions, and a…
Let $k$ be an algebraically closed field of characteristic $0$ and $A$ a graded $k$-algebra finitely generated in degree $1$. In this paper, for $3$-dimensional quadratic AS-regular algebras except for Type EC, we give a complete list of…
This is a brief survey of recent results by the authors devoted to one of the most important operators of integral geometry. Basic facts about the analytic family of cosine transforms on the unit sphere and the corresponding Funk transform…
The Algebra of Physical Space (APS) is used to explore the Constructive Standard Model (CSM) of particle physics. Namely, this paper connects the spinor formalism of the APS to massive amplitudes in the CSM. A novel equivalency between…
We study local algebras, which are structures similar to $\mathbb{Z}$-graded algebras concentrated in degrees $-1,0,1$, but without a product defined for pairs of elements at the same degree $\pm1$. To any triple consisting of a Kac-Moody…
We introduce generalized Schur functions and generalized positive functions in setting of slice hyperholomorphic functions and study their realizations in terms of associated reproducing kernel Pontryagin spaces
We show that in analogy to the introduction of Poisson structures twisted by a closed 3-form by Park and Klimcik-Strobl, the study of three dimensional sigma models with Wess-Zumino term leads in a likewise way to twisting of Courant…
In this article we investigate harmonicity, Laplacians, mean value theorems and related topics in the context of quaternionic analysis. We observe that a Mean Value Formula for slice regular functions holds true and it is a consequence of…
The ring of symmetric functions $\Lambda$, with natural basis given by the Schur functions, arise in many different areas of mathematics. For example, as the cohomology ring of the grassmanian, and as the representation ring of the…
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…
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…
Building from ideas of hypercomplex analysis on the quaternionic unit ball, we introduce Hermitian, Riemannian and K\"ahler-like structures on the latter. These are built from the so-called regular M\"obius transformations. Such geometric…