Related papers: Limiting behavior of determinantal point processes…

We study the problem raised in [Marco Stevens, Equivalent symmetric kernels of determinantal point processes, RMTA, 10(03):2150027, 2021] concerning the extension of its main result to the more general (potentially non-symmetric) setting.…

For any bounded regular domain $\Omega$ of a real analytic Riemannian manifold $M$, we denote by $\lambda_{k}(\Omega)$ the $k$-th eigenvalue of the Dirichlet Laplacian of $\Omega$. In this paper, we consider $\lambda_k$ and as a functional…

Let L be a holomorphic line bundle over a compact complex projective Hermitian manifold X. Any fixed smooth hermitian metric h on L induces a Hilbert space structure on the space of global holomorphic sections with values in the k th tensor…

Filtration of quantifiable objects by smoothing kernels on Riemannian manifolds for visualisation is an ongoing research. However, using common filters created for linear domains on manifolds with non-Euclidean topologies can yield…

We study the limit behaviour of singularly-perturbed elliptic functionals of the form \[ \mathcal F_k(u,v)=\int_A v^2\,f_k(x,\nabla u)\.dx+\frac{1}{\varepsilon_k}\int_A g_k(x,v,\varepsilon_k\nabla v)\.dx\,, \] where $u$ is a vector-valued…

We study kernel functions, and associated reproducing kernel Hilbert spaces $\mathscr{H}$ over infinite, discrete and countable sets $V$. Numerical analysis builds discrete models (e.g., finite element) for the purpose of finding…

In this paper, we first characterize the polar decomposition of unbounded weighted composition operator pairs $\textbf{C}_{\phi,\omega}$ in an $L^2$-space. Based on this characterization, we introduce the $\lambda$-spherical mean transform…

In this paper we consider the reproducing kernel thesis for boundedness and compactness for various operators on Bergman-type spaces. In particular, the results in this paper apply to the weighted Bergman space on the unit ball, the unit…

We consider the Laplace-Beltrami operator $\Delta_g$ on a smooth, compact Riemannian manifold $(M,g)$ and the determinantal point process $\mathcal{X}_{\lambda}$ on $M$ associated with the spectral projection of $-\Delta_g$ onto the…

If $\varphi$ is an analytic function from the unit disk $\mathbb{D}$ to itself, and $\varphi$ is not a conformal automorphism, we denote by $\lambda_{\varphi}$ its Denjoy-Wolff point, that is, the limit of the iterates…

Determinantal point processes (DPPs) are repulsive point processes where the interaction between points depends on the determinant of a positive-semi definite matrix. In this paper, we study the limiting process of L-ensembles based on…

We demonstrate that the weight operator associated with a submultiplicative filtration on the section ring of a polarized complex projective manifold is a Toeplitz operator. We further analyze the asymptotics of the associated weighted…

Let $\Omega$ be an unbounded, pseudoconvex domain in $\Bbb C^n$ and let $\varphi$ be a $\mathcal C^2$-weight function plurisubharmonic on $\Omega$. We show both necessary and sufficient conditions for existence and compactness of a weighted…

Let Y be an infinite covering space of a projective manifold M in P^N of dimension n geq 2. Let C be the intersection with M of at most n-1 generic hypersurfaces of degree d in P^N. The preimage X of C in Y is a connected submanifold. Let…

Let $X$ be a Banach space, let $(\Omega,\mu)$ be a $\sigma$-finite measure space and let $A,B\colon\Omega\to B(X)$ be strongly measurable $\gamma$-bounded functions. We show that for all $x\in X$ and all $x^*\in X^*$, there exist a Hilbert…

Let $\Omega$ be a piecewise-smooth, bounded convex domain in $\R^2$ and consider $L^2$-normalized Neumann eigenfunctions $\phi_{\lambda}$ with eigenvalue $\lambda^2$. Our main result is a small-scale {\em non-concentration} estimate: We…

The Cartan-Hartogs domains are defined as a class of Hartogs type domains over irreducible bounded symmetric domains. The purpose of this paper is twofold. Firstly, for a Cartan-Hartogs domain $\Omega^{B^{d_0}}(\mu)$ endowed with the…

We show how to build a kernel \[ K_X(x,y)=\sum_{m=0}^Xh(\lambda_m/{\lambda_X})\varphi_m(x)\overline{\varphi_m(y)} \] on a compact Riemannian manifold $M$, which is positive up to a negligible error and such that $K_X(x,x)\approx X$. Here…

It is shown that the property of being bounded below (having closed range) of weighted composition operators on Hardy and Bergman spaces can be tested by their action on a set of simple test functions, including reproducing kernels. The…

The main result of this paper is that determinantal point processes on the real line corresponding to projection operators with integrable kernels are quasi-invariant, in the continuous case, under the group of diffeomorphisms with compact…