Related papers: Propagation of regularity and positive definitenes…
We give a new proof of a classical result which provides a one-to-one correspondence between positive definite radial kernels on a homogeneous tree and finite Borel measures on the interval $[-1,1]$. Our methods allow us to find a new…
We provide a universal characterization of the construction taking a scheme $X$ to its stable $\infty$-category $\text{Mot}(X)$ of noncommutative motives, patterned after the universal characterization of algebraic K-theory due to…
The Newlander-Nirenberg theorem says that a formally integrable complex structure is locally equivalent to the standard complex structure in the complex Euclidean space. In this paper, we consider two natural generalizations of the…
In this paper we study continuous kernels on compact two point homogeneous spaces which are positive definite and zonal (isotropic). Such kernels were characterized by R. Gangolli some forty years ago and are very useful for solving…
In this paper we continue to investigate a certain class of Hankel-like positive definite kernels using their associated orthogonal polynomials. The main result of this paper is about the structure of this kind of kernels.
In this article we study properly discontinuous actions on Hilbert manifolds giving new examples of complete Hilbert manifolds with nonnegative, respectively nonpositive, sectional curvature with infinite fundamental group. We also get…
We give extensions of results on nonnegative matrix semigroups which deduce finiteness or boundedness of such semigroups from the corresponding local properties, e.g., from finiteness or boundedness of values of certain linear functionals…
In this paper, we describe the structure of shape derivatives around sets which are only assumed to be of finite perimeter in $\R^N$. This structure allows us to define a useful notion of positivity of the shape derivative and we show it…
We introduce a construction of multiscale tight frames on general domains. The frame elements are obtained by spectral filtering of the integral operator associated with a reproducing kernel. Our construction extends classical wavelets as…
A group is coherent if all its finitely generated subgroups are finitely presented. In this article we provide a criterion for positively determining the coherence of a group. This criterion is based upon the notion of the perimeter of a…
A classical result in complex geometry says that the automorphism group of a manifold of general type is discrete. It is more generally true that there are only finitely many surjective morphisms between two fixed projective manifolds of…
Let R be an affine algebra of dimension n \geq 3 over an algebraically closed field k. Suppose char k =0 or char k =p \geq n. Let g,f_1,...,f_r be a R-regular sequence and A=R[f_1/g,...,f_r/g]. Let P be a projective A-module of rank n-1…
We consider Delone sets with finite local complexity. We characterize validity of a subadditive ergodic theorem by uniform positivity of certain weights. The latter can be considered to be an averaged version of linear repetitivity. In this…
We study the category of GL-equivariant modules over the infinite exterior algebra in positive characteristic. Our main structural result is a shift theorem a la Nagpal. Using this, we obtain a Church--Ellenberg type bound for the…
We prove a new kind of homological stability theorem for automorphism groups of finitely-generated projective modules over Dedekind domains, which takes into account all possible stabilisation maps between these, rather than only…
We introduce the notion of positivity for a real basic $(1,1)$ class in basic Bott-Chern cohomology group on foliated manifolds, and study the relationship between this positivity and the negativity of transverse holomorphic sectional…
We present a method for constructing global holomorphic peak functions from local holomorphic support functions for broad classes of unbounded domains. As an application, we establish a method for showing the positivity and completeness of…
We propose a criterion for preserving the regularity of a formal language representation when passing from groups to subgroups. We use this criterion to show that the regularity of a positive cone language in a left-orderable group passes…
The distributional statistical framework replaces classical probability densities by distribution-kernel pairs $(T, \varphi)$, where $T$ is a tempered distribution and $\varphi$ is a rapidly decaying kernel. We develop the thesis that the…
We study regularity properties of CR maps in positive codimension valued in pseudoconvex manifolds which carry a nontrivial Levi foliation. We introduce an invariant which can be used to deduce that any sufficiently regular CR map from a…