Related papers: Q-valued functions revisited

We consider multivalued maps between $\Omega \subset \mathbb{R}^N$ open ($N \ge 2$) and a smooth, compact Riemannian manifold $\mathcal{N}$ locally minimizing the Dirichlet energy. An interior partial H\"older regularity result in the…

For every $q\in(0,1)$ and $0\le \alpha<1$ we define a class of analytic functions, the so-called $q$-starlike functions of order $\alpha$, on the open unit disk. We study this class of functions and explore some inclusion properties with…

In this note we prove an abstract version of a recent quantitative stratifcation priciple introduced by Cheeger and Naber (Invent. Math., 191 (2013), no. 2, 321-339; Comm. Pure Appl. Math., 66 (2013), no. 6, 965-990). Using this general…

We propose to study deformation quantizations of Whitney functions. To this end, we extend the notion of a deformation quantization to algebras of Whitney functions over a singular set, and show the existence of a deformation quantization…

A previously established correspondence between definite-parity real functions and inner analytic functions is generalized to real functions without definite parity properties. The set of inner analytic functions that corresponds to the set…

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,…

We introduce a new family of symmetric functions, which are $q$-analogues of products of Schur functions defined in terms of ribbon tableaux. These functions can be interpreted in terms of the Fock space representation of the quantum affine…

In this paper we study some fundamental algebraic properties of slice functions and slice regular functions over an alternative $^*$-algebra $A$ over $\mathbb{R}$. These recently introduced function theories generalize to higher dimensions…

In a recent important paper, Hoffstein and Hulse generalized the notion of Rankin-Selberg convolution $L$-functions by defining shifted convolution $L$-functions. We investigate symmetrized versions of their functions. Under certain mild…

The Hilbert functions of sets of distinct points in P^n have been characterized. We show that if we restrict to sets of distinct of points in P^{n_1} x ... x P^{n_k} that are also arithmetically Cohen-Macaulay (ACM for short), then there is…

For every natural number k we introduce the notion of k-th order convolution of functions on abelian groups. We study the group of convolution preserving automorphisms of function algebras in the limit. It turns out that such groups have…

I continue the investigation of a q-analogue of the convolution on the line started in a joint work with Koornwinder and based on a formal definition due to Kempf and Majid. Two different ways of approximating functions by means of the…

For large enough (but fixed) prime powers $q$, and trace functions to squarefree moduli in $\mathbb{F}_q[u]$ with slopes at most $1$ at infinity, and no Artin--Schreier factors in their geometric global monodromy, we come close to…

We show a Dvoretsky-Rogers type Theorem for the adapted version of the $q$-summing operators to the topology of the convergence of the vector valued integrals on Banach function spaces. In the pursuit of this objective we prove that the…

We introduce a new generalization of Stirling numbers of the second kind and analyze their properties, including generating functions, integral representations, and recurrence relations. These numbers are used to approximate Riemann zeta…

In a previous paper, the second author defined integer-valued functions delta_n on the first cohomology of a 3-manifold, generalizing McMullen's Alexander norm. It was shown that these functions give lower bounds on the Thurston norm. In…

We unite two well known generalisations of the Wadge theory. The first one considers more general reducing functions than the continuous functions in the classical case, and the second one extends Wadge reducibility from sets (i.e.,…

For a set $M$ of $m$ elements, we define a decreasing chain of classes of normalized monotone-increasing valuation functions from $2^M$ to $\mathbb{R}_{\geq 0}$, parameterized by an integer $q \in [2,m]$. For a given $q$, we refer to the…

Q-functions are widely used in discrete-time learning and control to model future costs arising from a given control policy, when the initial state and input are given. Although some of their properties are understood, Q-functions…

First some old as well as new results about P.I. algebras, Ore extensions, and degrees are presented. Then quantized $n\times r$ matrices as well as quantized factor algebras of $M_q(n)$ are analyzed. The latter are the quantized function…