Related papers: A Direct Connection Between the Bergman and Szeg\H…
The analysis of holomorphic sections of high powers $L^N$ of holomorphic ample line bundles $L\to M$ over compact K\"ahler manifolds has been widely applied in complex geometry and mathematical physics. The Tian-Yau-Zelditch's asymptotic…
The main objective of the present paper is to set up the theoretical basis and the language needed to deal with the problem of direct images of hermitian vector bundles for projective non-necessarily smooth morphisms. To this end, we first…
In this paper we study the Bergman kernel and projection on the unbounded worm domain $$ \mathcal{W}_\infty = \big\{(z_1,z_2)\in\mathbb{C}^2 : \big|z_1-e^{i\log|z_2|^2}\big|^2<1, z_2\neq0\big\}. $$ We first show that the Bergman space of…
We introduce a new biholomorphically invariant metric based on Fefferman's invariant Szego kernel and investigate the relation of the new metric to the Bergman and Carath\'eodory metrics. A key tool is a new absolutely invariant function…
We construct fully-discrete schemes for the Benjamin-Ono, Calogero-Sutherland DNLS, and cubic Szeg\H{o} equations on the torus, which are $\textit{exact in time}$ with $\textit{spectral accuracy}$ in space. We prove spectral convergence for…
Sheaf cohomology or, more generally, higher direct images of coherent sheaves along proper morphisms are central to modern algebraic geometry. However, the computation of these objects is a non-trivial and expensive task which easily…
The projection onto the intersection of sets generally does not allow for a closed form even when the individual projection operators have explicit descriptions. In this work, we systematically analyze the projection onto the intersection…
For a bounded domain $D \subset \mathbb{C}^n$, let $K_D = K_D(z) > 0$ denote the Bergman kernel on the diagonal and consider the reproducing kernel Hilbert space of holomorphic functions on $D$ that are square integrable with respect to the…
In this paper we continue to explore the connection between tensor algebras and displacement structure. We focus on recursive orthonormalization and we develop an analogue of the Szego type theory of orthogonal polynomials in the unit…
A new method of connecting two wavelet sets with a continuous path of wavelet sets is given. The method is based on a pure set theoretic fact known as the Schroder-Cantor-Bernstein theorem and on a characterization of wavelet sets in terms…
We exploit the equality of Bergman analytic content and torsional rigidity of a simply connected domain to develop a new method for calculating these quantities. This method is particularly suitable for the case when the region in question…
We study the asymptotics of Ohsawa-Takegoshi extension operator and orthogonal Bergman projector associated with high tensor powers of a positive line bundle. More precisely, for a fixed complex submanifold in a complex manifold, we…
We show connections between a special type of addition formulas and a theorem of Stieltjes and Rogers. We use different techniques to derive the desirable addition formulas. We apply our approach to derive special addition theorems for…
We apply integral representations for functions on non-smooth strictly pseudoconvex domains, the Henkin-Leiterer domains, to derive weighted $C^k$ estimates for the component of a given function, $f$, which is orthogonal to holomorphic…
We define Szego coordinates on a finitely connected smoothly bounded planar domain which effect a holomorphic change of coordinates on the domain that can be as close to the identity as desired and which convert the domain to a quadrature…
Hedgehogs are geometrical objects that describe the Minkowski differences of arbitrary convex bodies in the Euclidean space $\mathbb{E}^n$. We prove that two hedgehogs in $\mathbb{E}^n, n \geq 3$, coincide up to a translation and a…
We establish a weighted $L^p$ norm estimate for the Bergman projection for a class of pseudoconvex domains. We obtain an upper bound for the weighted $L^p$ norm when the domain is, for example, a bounded smooth strictly pseudoconvex domain,…
Let $(X, T^{1,0}X)$ be a compact connected orientable strongly pseudoconvex CR manifold of dimension $2n+1$, $n\geq1$. Assume that $X$ admits a connected compact Lie group $G$ action and a transversal CR $S^1$ action, we compute the…
We describe a notion of ampleness for line bundles on orbifolds with cyclic quotient singularities that is related to embeddings in weighted projective space, and prove a global asymptotic expansion for a weighted Bergman kernel associated…
The bicomplex Bergman spaces are studied for any bounded bicomplex domain. Its Bergman kernel is computed in terms of the kernels of the complex projections of the domain. We also introduce two additional reproducing kernel Hilbert spaces…