Related papers: Q-valued functions revisited
We prove a Carleman-type estimate for Dirichlet-stationary multivalued functions and apply it to give a different proof of the optimal dimension of the singular set of Dir-minimizing multivalued functions, originally due to Almgren and to…
We consider the H\"older continuity for the Dirichlet problem at the boundary. Almgren introduced the multivalued; Q-valued functions for studying regularity of minimal surfaces in higher codimension. The H\"older continuity in the interior…
We provide new elementary proofs of the following two results: every complex variety is locally the graphs of a Dir-minimizing function, first proved by Almgren; the gradients of Dir-minimizing functions, in principle square-summable, are…
In this paper, we extend the related notions of Dirichlet quasiminimizer, $\omega-$minimizer and almost minimizer to the framework of multiple-valued functions in the sense of Almgren and prove Holder regularity results. We also give…
We consider general integral functionals on the Sobolev spaces of multiple valued functions, introduced by Almgren. We characterize the semicontinuous ones and recover earlier results of Mattila as a particular case. Moreover, we answer…
We present examples of holomorphic functions that vanish to in- finite order at points at the boundary of their domain of definition. They give rise to examples of Dirichlet minimizing Q-valued functions indicating that "higher"-regularity…
We study the algebraic $K$-theory of the ring of continuous functions on a compact Hausdorff space with values in a local division ring, e.g., a local field: We compute its negative $K$-theory and show its $K$-regularity. The complex case…
The paper deals with particular classes of $q\times q$ matrix-valued functions which are holomorphic in $\mathbb{C}\setminus[\alpha,+\infty)$, where $\alpha$ is an arbitrary real number. These classes are generalizations of classes of…
We prove several results on Almgren's multiple valued functions and their links to integral currents. In particular, we give a simple proof of the fact that a Lipschitz multiple valued map naturally defines an integer rectifiable current;…
We present closed forms for several functions that are fundamental in number theory and we explain the method used to obtain them. Concretely, we find formulas for the p-adic valuation, the number-of-divisors function, the sum-of-divisors…
Motivated by recent interest on Kirchhoff-type equations, in this short note we utilize a classical, yet very powerful, tool of nonlinear functional analysis in order to investigate the existence of positive eigenvalues of systems of…
This study utilizes Orlicz functions to provide refined lower and upper bounds on the q-numerical radius of an operator acting on a Hilbert space. Additionally, the concept of q-sectorial matrices is introduced and further bounds for the…
We use derived Hall algebra of the category of nilpotent representations of Jordan quiver to reconstruct the theory of symmetric functions, focusing on Hall-Littlewood symmetric functions and various operators acting on them.
The paper considers the representation of k-valued logical functions in the class of disjunctive normal forms. Various classes of monotone functions of k-valued logic are investigated. Theorems are proved on the coincidence of reduced and…
The classical concept of $Q$-functions associated to symmetric and selfadjoint operators due to M.G. Krein and H. Langer is extended in such a way that the Dirichlet-to-Neumann map in the theory of elliptic differential equations can be…
We consider several systems of algebras of real- and complex-valued functions, which appear in o-minimal geometry and related geometrically tame contexts. For each such system, we prove its stability under parametric integration and we…
In this note we give a quantitative estimate on the number of singular points of multiplicity $Q$ of a $2$-dimensional $Q$-valued energy minimizing map, in terms of the value of its frequency function.
We define an axiomatic class of L-functions extending the Selberg class. We show in particular that one can recast the traditional conditions of an Euler product, analytic continuation and functional equation in terms of distributional…
In this work, we review and extend some well known results for the eigenvalues of the Dirichlet $p-$Laplace operator to a more general class of monotone quasilinear elliptic operators. As an application we obtain some homogenization results…
We study algebraic discrete valuations dominating normal local domains of dimension two. We construct a family of examples to show that the Hilbert-Samuel function of the associated graded ring of the valuation can fail to be asymptotically…