Related papers: Holomorphic Function Spaces on Homogeneous Siegel …

Let D be a Hartogs domain of the form D={(z,w) \in CxC^N : |w| < e^{-u(z)}} where u is a subharmonic function on C. We prove that the Bergman space of holomorphic and square integrable functions on D is either trivial or infinite…

We study the geometry of homogeneous hypersurfaces and their focal sets in complex hyperbolic spaces. In particular, we provide a characterization of the focal set in terms of its second fundamental form and determine the principal…

In this article, the Hodge decomposition for any degree of differential forms is investigated on the whole space $\mathbb{R}^n$ and the half-space $\mathbb{R}^n_+$ on different scale of function spaces namely homogeneous and inhomogeneous…

The purpose of this paper is to study sparse domination estimates of composition operators in the setting of complex function theory. The method originates from proofs of the $A_2$ theorem for Calder\'on-Zygmund operators in harmonic…

In 1990 van Eijnghoven and Meyers introduced systems of holomorphic Hermite functions and reproducing kernel Hilbert spaces associated with the systems on the complex plane. Moreover they studied the relationship between the family of all…

We present simple examples of finite-dimensional connected homogeneous spaces (they are actually topological manifolds) with nonhomogeneous and nonrigid factors. In particular, we give an elementary solution of an old problem in general…

Let $({\mathcal X},d,\mu)$ be a metric measure space of homogeneous type in the sense of R. R. Coifman and G. Weiss and $H^1_{\rm at}({\mathcal X})$ be the atomic Hardy space. Via orthonormal bases of regular wavelets and spline functions…

A finite dimensional system with a quadratic Hamiltonian constraint is Dirac quantized in holomorphic, antiholomorphic and mixed representations. A unique inner product is found by imposing Hermitian conjugacy relations on an operator…

The extended weight semigroup of a homogeneous space G/H of a connected semisimple algebraic group G characterizes the spectra of the representations of G on the spaces of regular sections of homogeneous linear bundles over G/H, including…

We construct explicit geometric models for moduli spaces of semi-stable strongly parabolic Higgs bundles over the Riemann sphere, in the case of rank two, four marked points, arbitrary degree, and arbitrary weights. The mechanism of…

Let $M$ be a non-compact connected Riemann surface of finite type, and $R\subset\subset M$ be a relatively compact domain such that $H_{1}(M,\Z)=H_{1}(R,\Z)$. Let $\tilde R\longrightarrow R$ be a covering. We study the algebra…

This paper is dedicated to weighted composition semigroups on spaces of continuous functions and their subspaces. We consider semigroups induced by semiflows and semicocycles on Banach spaces $\mathcal{F}(\Omega)$ of continuous functions on…

We study the simultaneous homogenization and dimension reduction of an energy functional with linear growth defined on the space of manifold valued Sobolev functions. The study is carried out by $\Gamma$-convergence, providing an integral…

We investigate homogeneity in the special Colombeau algebra. It is shown that strongly scaling invariant functions on the d-dimensional space are simply the constants. On the pierced space, strongly homogeneous functions admit tempered…

For smoothly bounded, strongly $\mathbb{C}$-convex domains, one can use the Fefferman form or its variants to define projectively invariant norms on sections of holomorphic line bundles, producing a Hardy space. In two variables, we…

We show that a weakly holomorphic modular function can be written as a sum of modular units of higher level. We further find a necessary and sufficient condition for a Siegel modular function of degree $g$ to have neither zero nor pole on…

Recently the author presented a new approach to solving the coefficient problems for holomorphic functions based on the deep features of Teichmuller spaces. It involves the Bers isomorphism theorem for Teichmuller spaces of punctured…

This is a part of our joint program. The purpose of this paper is to study smooth toroidal compactifications of Siegel varieties and their applications, we also try to understand the K\"ahler-Einstein metrics on Siegel varieties through the…

We consider spaces for which there is a notion of harmonicity for complex valued functions defined on them. For instance, this is the case of Riemannian manifolds on one hand, and (metric) graphs on the other hand. We observe that it is…

In the spirit of the geometric approach to two-dimensional conformal field theory, we explicitly associate to every holomorphic vertex operator algebra a section of a power of Hodge line bundle on the moduli space of curves of arbitrary…