Related papers: Borel-Carath\'{e}odory Type Theorem for monogenic …
We discuss generalised duality theory for monoidal categories and its applications to the categories of exact endofunctors, graded vector spaces, and topological vector spaces.
We construct a Moutard-type transform for the generalized analytic functions. The first theorems and the first explicit examples in this connection are given.
We consider a class of $n^{\text{th}}$-order linear ordinary differential equations with a large parameter $u$. Analytic solutions of these equations can be described by (divergent) formal series in descending powers of $u$. We demonstrate…
We survey recent results about the Torelli question for holomorphic-symplectic varieties. Following are the main topics. A Hodge theoretic Torelli theorem. A study of the subgroup W, of the isometry group of the weight 2 Hodge structure,…
We begin by reviewing a classical result on the algebraic dependence of commuting elements in Weyl algebras. We proceed by describing generalizations of this result to various classes of Ore extensions, both results that have already been…
The general linear quaternion function of degree one is a sum of terms with quaternion coefficients on the left and right. The paper considers the canonic form of such a function, and builds on the recent work of Todd Ell, who has shown…
A theorem of Maurer-Cartan type for Lie algebroids is presented. Suppose that any vector subbundle of a Lie algebroid is called interior differential system (IDS) for that Lie algebroid. A theorem of Cartan type is obtained. Extending the…
In the paper [1] we consider a new class, so-called, $G$-monogenic (differentiable in the sense of Gateaux) quaternionic mappings. In the present paper we introduce quaternionic $H$-monogenic (differentiable in the sense of Hausdorff)…
The concept of generalized partial-slice monogenic functions has been recently introduced to include the two theories of monogenic functions and of slice monogenic functions over Clifford algebras. The main purpose of this article is to…
The main goal in this manuscript is to present a class of functions satisfying a certain orthogonality property for which there also exists a three term recurrence formula. This class of functions, which can be considered as an extension to…
In this paper we prove a generalization of Montel's theorem for a class of first order elliptic equations with measurable coefficients involving Hodge-Dirac operators. We then apply this result to sequences of solutions of second order…
We define the monoidal category $(Poly_E,y,\triangleleft)$ of polynomials under composition in any category $E$ with finite limits, including both cartesian and vertical morphisms of polynomials, and generalize to this setting the Dirichlet…
We give a criterium of holomorphy for some type formal power series. This gives a stronger form of a Rothstein's type extension theorem for a particular ring of holomorphic functions.
The Bohr theorem states that any function $f(z) = \sum_{n=0}^{\infty} a_{n} z^{n}$, analytic and bounded in the open unit disk, obeys the inequality $\sum_{n=0}^{\infty} |a_{n}| |z|^{n} < 1$ in the open disk of radius 1/3, the so-called…
In a recent paper, we introduced the concept of generalized partial-slice monogenic functions. The class of these functions includes both the theory of monogenic functions and of slice monogenic functions with values in a Clifford algebra.…
Generalized operads, also called generalized multicategories and $T$-monoids, are defined as monads within a Kleisli bicategory. With or without emphasizing their monoidal nature, generalized operads have been considered by numerous authors…
We prove a quantitative openness theorem for $C^1$ submersions under suitable assumptions on the differential. We then apply our result to a class of exponential maps appearing in Carnot-Carath\'eodory spaces and we improve a classical…
In this paper we show how the theory of monads can be used to deduce in a uniform manner several duality theorems involving categories of relations on one side and categories of algebras with homomorphisms preserving only some operations on…
Operads may be represented as symmetric monoidal functors on a small symmetric monoidal category. We discuss the axioms which must be imposed on a symmetric monoidal functor in order that it give rise to a theory similar to the theory of…
This work proposes a unified theory of regularity in one hypercomplex variable: the theory of $T$-regular functions. In the special case of quaternion-valued functions of one quaternionic variable, this unified theory comprises…