Related papers: Strong Hamel functions and symmetries
In this paper, we study global properties of continuous plurisubharmonic functions on complete noncompact K\"ahler manifolds with nonnegative bisectional curvature and their applications to the structure of such manifolds. We prove that…
We characterize a holomorphic positive definite function $f$ defined on a horizontal strip of the complex plane as the Fourier-Laplace transform of a unique exponentially finite measure on $\mathbb{R}$. The classical theorems of Bochner on…
Graphical functions are positive functions on the punctured complex plane $\mathbb{C}\setminus\{0,1\}$ which arise in quantum field theory. We generalize a parametric integral representation for graphical functions due to Lam, Lebrun and…
We consider classes $ \mathcal{A}_M(S) $ of functions holomorphic in an open plane sector $ S $ and belonging to a strongly non-quasianalytic class on the closure of $ S $. In $ \mathcal{A}_M(S) $, we construct functions which are flat at…
In this paper we consider a special kind of three-point functions of HHL type at weak coupling in N=4 SYM theory and analyze its volume dependence. At strong coupling this kind of three-point functions were studied recently by Bajnok, Janik…
We define a free holomorphic function to be a function that is locally a bounded nc-function. We prove that free holomorphic functions are the functions that are locally uniformly approximable by free polynomials. We prove a realization…
Let X be a Stein manifold, and let Y be a closed complex submanifold of X. Denote by O(X) the algebra of holomorphic functions on X. We show that the weak (i.e., flat) homological dimension of O(Y) as a Fr'echet O(X)-module equals the…
The extended Schur functions form a basis of quasisymmetric functions that contains the Schur functions. We provide a representation-theoretic interpretation of this basis by constructing $0$-Hecke modules whose quasisymmetric…
Let $\Omega\subset\mathbb{C}^n$ be a bounded domain with smooth boundary, whose Bergman projection $B$ maps the Sobolev space $H^{k_{1}}(\Omega)$ (continuously) into $H^{k_{2}}(\Omega)$. We establish two smoothing results: (i) the full…
Determining functionals are tools to describe the finite dimensional long-term dynamics of infinite dimensional dynamical systems. There also exist several applications to infinite dimensional {\em random} dynamical systems. In these…
We analyze integral representation and $\Gamma$-convergence properties of functionals defined on \emph{piecewise rigid functions}, i.e., functions which are piecewise affine on a Caccioppoli partition where the derivative in each component…
A holomorphy potential is a complex valued function whose complex gradient, with respect to some K\"ahler metric, is a holomorphic vector field. Given $k$ holomorphic vector fields on a compact complex manifold, form, for a given K\"ahler…
Sufficient conditions are given for a hard implicit function theorem to hold. The result is established by an application of the Dynamical Systems Method (DSM). It allows one to solve a class of nonlinear operator equations in the case when…
We study functional stochastic differential equations with a locally unbounded, functional drift focusing on well-posedness, stability and the strong Feller property. Following the non-functional case, we only consider integrability…
The main purpose of the present paper is to introduce the notion of squeezing functions of bounded domains and study some properties of them. The relation to geometric and analytic structures of bounded domains will be investigated.…
In this paper we introduce some {\it variation functions} associated to the rank of the Infinitesimal Variations of Hodge Structure for a family of smooth projective complex curves. We give some bounds and inequalities and, in particular,…
Assuming the Riemann hypothesis, we prove the weak convergence of linear statistics of the zeros of L-functions towards a Gaussian field, with covariance structure corresponding to the $\HH^{1/2}$-norm of the test functions. For this…
The symmetric function theorem states that a polynomial that is invariant under permutation of variables, is a polynomial in the elementary symmetric polynomials. We deduce this classical result, in the analytic setting, from the…
We define the class of high dimensional graph manifolds. These are compact smooth manifolds supporting a decomposition into finitely many pieces, each of which is diffeomorphic to the product of a torus with a finite volume hyperbolic…
Let M be a simply-connected complete Kahler manifold whose sectional curvature is bounded between two negative numbers. In this paper we prove the existence of non-constant bounded holomorphic functions on M if the complex dimension of M is…