相关论文: On the Bergman projection and kernel in periodic p…
This paper proposes a novel beamforming framework in the reproducing kernel domain, derived from a unified interpretation of directional response as spatial differentiation of the sound field. By representing directional response using…
This paper considers the problem of $L^p$-estimates for a certain multilinear functional involving integration against a kernel with the structure of a determinant. Examples of such objects are ubiquitous in the study of Fourier restriction…
The aim of the present thesis is twofold: to study the problem of discreteness of the spectrum of Schr\"odinger operators with matrix-valued potentials in ${\mathbb R}^d$ (Chapter 1), and to prove new pointwise bounds for weighted Bergman…
In this paper we study mapping properties of Toeplitz-like operators on weighted Bergman spaces of bounded strongly pseudconvex domains in $\mathbb{C}^n$. In particular we prove that a Toeplitz operator built using as kernel a weighted…
We study the procedure of regularization in the context of the Lipschitz version of de Rham calculus on metric simplicial complexes with bounded geometry. It provides us with the machinery to handle the de Rham homomorphism for…
Given a real-analytic function b(x) defined on a neighborhood of the origin with b(0) = 0, we consider local convolutions with kernels which are bounded by |b(x)|^(-a), where a > 0 is the smallest number for which |b(x)|^(-a) is not…
In terms of layer potential methods, this paper is devoted to study the $L^2$ boundary value problems for nonhomogeneous elliptic operators with rapidly oscillating coefficients in a periodic setting. Under a low regularity assumption on…
We study the boundedness of Toeplitz operators with locally integrable symbols on Bergman spaces $A^p(\Omega),$ $1<p<\infty,$ where $\Omega\subset \mathbb{C}$ is a bounded simply connected domain with polygonal boundary. We give sufficient…
We establish $L^p$-boundedness for a class of operators that are given by convolution with product kernels adapted to curves in the space. The $L^p$ bounds follow from the decomposition of the adapted kernel into a sum of two kernels with…
We present the theory of Cauchy-Fantappi\'e integral operators, with emphasis on the situation when the domain of integration, $D$, has minimal boundary regularity. Among these operators we focus on those that are more closely related to…
The analysis of the dependence of integral operators on perturbations plays an important role in the study of inverse problems and of perturbed boundary value problems. In this paper we focus on the mapping properties of the volume…
We deal with a class of one-parameter family of integral transforms of Bargmann type arising as dual transforms of fractional Hankel transform. Their ranges are identified to be special subspaces of the weighted hyperholomorphic left…
For any $\pi$-formal group scheme $G$, the Frobenius morphism between arithmetic jet spaces restricts to generalized kernels of the projection map. Using the functorial properties of such kernels of arithmetic jet spaces, we show that this…
The main purpose of our paper is a new approach to design of algorithms of Kaczmarz type in the framework of operators in Hilbert space. Our applications include a diverse list of optimization problems, new Karhunen-Lo\`eve transforms, and…
Needlets have been recognized as state-of-the-art tools to tackle spherical data, due to their excellent localization properties in both spacial and frequency domains. This paper considers developing kernel methods associated with the…
We show that all smooth ring domains $\Omega\subset \mathbb{R}^2$ that admit a solution to Serrin's classical problem $\Delta u+2=0$ with locally constant overdetermined boundary conditions along $\partial \Omega$ can be described as…
We prove the boundedness of Bergman type projections in two different analytic function spaces in bounded strongly pseudoconvex domains with the smooth boundary. Our results were previously well-known in the case of the unit disk.
In this article, we investigate the connection between certain real variable things and the Bergman theory. We first use Hardy-type inequalities to give an $L^2$ Hartogs-type extension theorem and an $L^p$ integrability theorem for the…
We look at the $L^p$ bounds on eigenfunctions for polygonal domains (or more generally Euclidean surfaces with conic singularities) by analysis of the wave operator on the flat Euclidean cone $C(\mathbb{S}^1_\rho) := \mathbb{R}_+ \times…
We study ordinal-indexed, multi-layer iterations of bounded operator transforms and prove convergence to spectral/ergodic projections under functional-calculus hypotheses. For normal operators on Hilbert space and polynomial or holomorphic…