相关论文: On generalized Vietoris' number sequences - origin…
We prove a compact embedding theorem in a class of spaces of piecewise H1 functions subordinated to a class of shape regular, but not necessarily quasi-uniform triangulations of a polygonal domain. This result generalizes the…
In this paper, we present the general one-dimensional Clifford Fourier Transform. We derive fundamental properties: Plancherel theorem, reconstruction and convolution formulas. Additionally, we provide an application to probability theory…
Fixed point theorems are one of the many tools used to prove existence and uniqueness of differential equations. When the data involved contains products of distributions, some of these tools may not be useful. Thus rises the necessity to…
$q$-Analogues of the coefficients of $x^a$ in the expansion of $\prod_{j=1}^N (1+x+...+x^j)^{L_j}$ are proposed. Useful properties, such as recursion relations, symmetries and limiting theorems of the ``$q$-supernomial coefficients'' are…
Fueter's theorem states, in modern terms, that the Laplacian maps slice-regular quaternionic functions into Fueter-regular functions with axial symmetry. This phenomenon is also present in the Clifford setting, where both slice-monogenic…
In this paper we show how to describe the general theory of a linear metric compatible connection with the theory of Clifford valued differential forms. This is done by realizing that for each spacetime point the algebra of Clifford…
The main purpose of this article is to present a generalization of Forelli's theorem for functions holomorphic along a suspension of integral curves of a diagonalizable vector field of aligned type. For this purpose, we develop a new…
In this paper we prove a quaternionic positive real lemma as well as its generalized version, in case the associated kernel has negative squares for slice hyperholomorphic functions. We consider the case of functions with positive real part…
This paper is concerned with the concept of linear repetitivity in the theory of tilings. We prove a general uniform subadditive ergodic theorem for linearly repetitive tilings. This theorem unifies and extends various known (sub)additive…
The purpose of the paper is three-fold: (a) we prove that every sequence which is a multidimensional sum of a balanced hypergeometric term has an asymptotic expansion of Gevrey type-1 with rational exponents, (b) we construct a class of…
In several different settings, one comes across situations in which the objects of study are locally consistent but globally inconsistent. Earlier work about probability distributions by Vorob'ev (1962) and about database relations by…
Inspired by subsequential ergodic theorems, we study the validity of Wiener's lemma and the extremal behavior of a measure $\mu$ on the unit circle via the behavior of its Fourier coefficients $\hat\mu(k_n)$ along subsequences $(k_n)$. We…
We study properties of coefficients of a linear form, originating from a multiple integral. As a corollary, we prove Vasilyev's conjecture, connected with the problem of irrationality of the Riemann zeta function at odd integers.
Supersymmetric backgrounds in M-theory often involve four-form flux in addition to pure geometry. In such cases, the classification of supersymmetric vacua involves the notion of generalized holonomy taking values in SL(32,R), the Clifford…
In this paper we prove that if a closed set in R^N is close to a cone over a simplicial complex at each point and at each scale, then it is locally bi-H\"older equivalent to such a cone. This generalizes Reifenberg's Topological Disk…
Operator systems connect operator algebra, free semialgebraic geometry and quantum information theory. In this work we generalize operator systems and many of their theorems. While positive semidefinite matrices form the underlying…
We introduce and study the generalized cyclotomic polynomials $\Phi_{A,S,n}(x)$ associated with a regular system $A$ of divisors and an arbitrary set $S$ of positive integers. We show that all of these polynomials have integer coefficients,…
In the first part of this paper, we establish some results around generalized Borel's Theorem. As an application, in the second part, we construct example of smooth surface of degree $d\geq 19$ in $\mathbb{CP}^3$ whose complements is…
We develop a class of uniformizations for certain weight 3 variations of Hodge structure (VHS). The analytic properties of the VHS are used to establish a conjecture of Eskin, Kontsevich, M\"oller, and Zorich on Lyapunov exponents.…
In this paper, we study a certain cohomology attached to a smooth function, which arose naturally in Poisson geometry. We explain how this cohomology depends on the function, and we prove that it satisfies both the excision and the…