Related papers: Matrix-Valued Corona Theorem for Multiply Connecte…
The main purpose of this paper is to extend and refine some work of Agler-McCarthy and Amar concerning the Corona problem for the polydisk and the unit ball in $\mathbb{C}^n$.
This survey contains a selection of topics unified by the concept of positive semi-definiteness (of matrices or kernels), reflecting natural constraints imposed on discrete data (graphs or networks) or continuous objects (probability or…
We establish results with an arithmetic flavor that generalize the polynomial multidimensional Szemeredi theorem and related multiple recurrence and convergence results in ergodic theory. For instance, we show that in all these statements…
Given a complex domain $\Omega$ and analytic functions $\varphi_1,\ldots,\varphi_n : \Omega \to \mathbb{D}$, we give geometric conditions for $H^\infty(\Omega)$ to be generated by functions of the form $g \circ \varphi_k$, $g \in…
We generalize some of the results in [arXiv: math.CV/0503430], and prove a bump-lemma for closed sets in semi 1-coronae. From this we obtain some finite cohomology results and an extension theorem for analytic subsets in 1-coronae.
In this paper we prove Morse index theorems for a big class of constrained variational problems on graphs. Such theorems are useful in various physical and geometric applications. Our formulas compute the difference of Morse indices of two…
The fine curve graph was introduced to study homeomorphism group of surfaces. In this paper we study the topology of the Gromov boundary of this graph for closed surfaces with higher genus. We first prove a bounded geodesic image theorem…
We characterize a rich class of valuated matroids, called R-minor valuated matroids that includes the indicator functions of matroids, and is closed under operations such as taking minors, duality, and induction by network. We exhibit a…
Knecht considers the enumeration of coronas. This is a counting problem for two specific types of lozenge tilings. Their exact closed formulas are conjectured in [A380346] and [A380416] on the OEIS. We prove this conjecture by using the…
In this note, simple proofs of certain well-known results involving the positive square root of positive matrices are given.
We introduce a new class of matroids, called graph curve matroids. A graph curve matroid is associated to a graph and defined on the vertices of the graph as a ground set. We prove that these matroids provide a combinatorial description of…
The Riemann Theorem states, that for any nontrivial connected and simply connected domain on the Riemann sphere there exists some its conformal bijection to the exterior of the unit disk. In this paper we find an explicit form of this map…
We consider the convergence of pointed multiply connected domains in the Caratheodory topology. Behaviour in the limit is largely determined by the properties of the simple closed hyperbolic geodesics which separate components of the…
We prove that the vector-valued generator of a bounded holomorphic semigroup represented by a kernel satisfying Gaussian estimates with bounded $H^\infty$-calculus in $L^2(\mathbb R^d;\mathbb C^m)$ admits bounded $H^\infty$-calculus for…
Given a rational function of degree at least two defined over a number field k, we study the cardinality of the set of rational iterated preimages. We prove bounds for the cardinality of this set as the rational function varies in certain…
We prove that a real-valued function (that is not assumed to be continuous) on a real analytic manifold is analytic whenever all its restrictions to analytic submanifolds homeomorphic to the 2-sphere are analytic. This is a real analog for…
Let M be a matroid on E, representable over a field of characteristic zero. We show that h-vectors of the following simplicial complexes are log-concave: 1. The matroid complex of independent subsets of E. 2. The broken circuit complex of…
We study projections in the corona algebra of $C(X)\otimes K$ where $X=[0,1],[0,\infty),(-\infty,\infty)$, and $[0,1]/\{0,1 \}$. Using BDF's essential codimension, we determine conditions for a projection in the corona algebra to be…
Let X be any generalized flag variety with Picard group of rank one. Given a degree d, consider the Gromov-Witten variety of rational curves of degree d in X that meet three general points. We prove that, if this Gromov-Witten variety is…
Two numerical algorithms are proposed for computing an interval matrix containing the matrix gamma function. In 2014, the author presented algorithms for enclosing all the eigenvalues and basis of invariant subspaces of $A \in \mathbb{C}^{n…