Related papers: The Bergman kernel and projection on non-smooth wo…

In this work, we study the Kuelbs-Steadman-2 space (KS-2 space), a Hilbert space constructed via the Henstock-Kurzweil integral, which allows handling non-absolutely integrable functions. We present the construction of the KS-2 space over…

Transposing the Berezin quantization into the setting of analytic microlocal analysis, we construct approximate semiclassical Bergman projections on weighted $L^2$ spaces with analytic weights, and show that their kernel functions admit an…

We obtain a full asymptotic expansion for orthogonal polynomials with respect to weighted area measure on a Jordan domain $\mathscr{D}$ with real-analytic boundary. The weight is fixed and assumed to be real-analytically smooth and strictly…

We give a characterization of $L_h^2$-domains of holomorphy with the help of the boundary behavior of the Bergman kernel and geometric properties of the boundary, respectively.

By applying the covariant Taylor expansion method, the fifth lower coefficients the asymptotic expansion of the heat kernel associated with a fermion of spin 1/2 in Riemann-Cartan space are manifestly given. These coefficients in…

We construct new $3$-dimensional variants of the classical Diederich-Fornaess worm domain. We show that they are smoothly bounded, pseudoconvex, and have nontrivial Nebenh\"{u}lle. We also show that their Bergman projections do not preserve…

Consider a bounded, strongly pseudoconvex domain $D\subset \mathbb C^n$ with minimal smoothness (namely, the class $C^2$) and let $b$ be a locally integrable function on $D$. We characterize boundedness (resp., compactness) in $L^p(D), p >…

This paper studies Fefferman's program \cite{F3} of expressing the singularity of the Bergman kernel, for smoothly bounded strictly pseudoconvex domains $\Omega\subset\C^n$, in terms of local biholomorphic invariants of the boundary. By…

There are very few general theorems on the kernel of the well-known Lichnerowicz Laplacian. In the present article we consider the geometry of the kernel of this operator restricted to covariant (not necessarily symmetric or skew-symmetric)…

We generalize the results of Montgomery for the Bochner Laplacian on high tensor powers of a line bundle. When specialized to Riemann surfaces, this leads to the Bergman kernel expansion and geometric quantization results for semi-positive…

In this article, we define a non-commutative deformation of the "symplectic invariants" of an algebraic hyperelliptical plane curve. The necessary condition for our definition to make sense is a Bethe ansatz. The commutative limit reduces…

We obtain necessary and sufficient conditions for the $L^p$-boundedness of the operator with positive Bergman kernel in some homogeneous Siegel domains of Cn. The key tool used here is the Okikiolu test, which finally leads to better result…

We give an extensive study on the Bergman kernel expansions and the random zeros associated with the high tensor powers of a semipositive line bundle on a complete punctured Riemann surface. We prove several results for the zeros of…

Let $\{M_j\}$ be a sequence of complete Riemannian surfaces which converges in the sense of Cheeger-Gromov to a complete Riemannian surface $M$. We study the convergence of the Bergman kernel $K_{M_j}$ of $M_j$ by using isoperimetric…

We present a technique for computing explicit, concrete formulas for the weighted Bergman kernel on a planar domain with weight the modulus squared of a meromorphic function in the case that the meromorphic function has a finite number of…

Let $({X}, \omega)$ be a compact $n$-dimensional K\"ahler orbifold, the stabilizer groups of which are abelian and have rank at most two. Let ${E}$ be an orbi-ample vector bundle of rank $2$ over ${X}$ and let $H$ be a Hermitian metric on…

We study the $\bar{\partial}_b$-Neumann problem for domains $\Omega$ contained in a strictly pseudoconvex manifold M^{2n+1} whose boundaries are noncharacteristic and have defining functions depending solely on the real and imaginary parts…

Let $M$ be a closed complex submanifold in ${\mathbb C}^N$ with the complete K\"ahler metric induced by the Euclidean metric. Several finiteness theorems on the $L^p$ Bergman space of holomorphic sections of a given Hermitian line bundle…

On a compact Kahler manifold, one can define global invariants by integrating local invariants of the metric. Assume that a global invariant thus obtained depends only on the Kahler class. Then we show that the integrand can be decomposed…

We prove a graph theoretic closed formula for coefficients in the Tian-Yau-Zelditch asymptotic expansion of the Bergman kernel. The formula is expressed in terms of the characteristic polynomial of the directed graphs representing Weyl…