Related papers: M-harmonic reproducing kernels on the ball
We ask whether a morphism $g$ in a triangulated category $C$ endowed with a weight structure "kills weights" (between an integer $m$ and some $n\ge m$). If $g=id_M$ (where $M\in Obj C$) and $C$ is Karoubian, then $g$ kills weights…
Using an estimate on the number of critical points for a Morse-even function on the sphere $\mathbb S^m$, $m\ge1$, we prove a multiplicity result for orthogonal geodesic chords in Riemannian manifolds with boundary that are diffeomorphic to…
Let $\Gamma\subset \mathrm{SU}((2,1),\mathbb{C})$ be a torsion-free cocompact subgroup. Let $\mathbb{B}^{2}$ denote the $2$-dimensional complex ball endowed with the hyperbolic metric $\mu_{\mathrm{hyp}}$, and let…
Balayage of measures with respect to classes of all subharmonic or harmonic functions on an open set of a plane or finite-dimensional Euclidean space is one of the main objects of potential theory and its applications to the complex…
A basic building block in Classical Potential Theory is the fundamental solution of the Laplace equation in ${\mathbb R}^d$ (Newtonian kernel). The main goal of this article is to study the rates of nonlinear $n$-term approximation of…
We introduce and study properties of certain new multifunctional harmonic spaces in the upper halfspace.We prove several sharp embedding theorems for such multifunctional spaces,these results are new even in the case of a single function.
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…
We characterize those generating functions k that produce weighted Hardy spaces of the unit disk D supporting nontrivial Hermitian weighted composition operators. Our characterization shows that the spaces associated with the "classical…
We present a conceptual and uniform interpretation of the methods of integral representations of L-functions (period integrals, Rankin-Selberg integrals). This leads to: (i) a way to classify of such integrals, based on the classification…
In this paper, we investigate the spectra of invertible weighted composition operators with automorphism symbols, on Hardy space $H^2(\mathbb{B}_N)$ and weighted Bergman spaces $A_\alpha^2(\mathbb{B}_N)$, where $\mathbb{B}_N$ is the unit…
We~prove uniqueness of the Moebius invariant semi-inner product on hyperbolic-harmonic functions on the unit ball of the real n-space, i.e. on functions annihilated by the hyperbolic Laplacian on the ball.
I discuss the relation between harmonic polynomials and invariant theory and show that homogeneous, harmonic polynomials correspond to ternary forms that are apolar to a base conic (the absolute). The calculation of Schlesinger that…
Given a compact complex manifold $Y$ with a negative line bundle $L\rightarrow Y$, we study the Schwarz-type symmetrization on the total space of $L$. We prove that this symmetrization does not increase the Monge-Amp\`{e}re energy for the…
A class of Riemann-Hilbert problems corresponding to quasi-permutation monodromy matrices is solved in terms of Szeg\"o kernel on auxiliary Riemann surfaces. The tau-function of Schlesinger system turns out to be closely related to…
In Part 1 we study the spherical functions on compact symmetric pairs of arbitrary rank under a suitable multiplicity freeness assumption and additional conditions on the branching rules. The spherical functions are taking values in the…
We introduce an extended Kepler-Coulomb quantum model in spherical coordinates. The Schr\"{o}dinger equation of this Hamiltonian is solved in these coordinates and it is shown that the wave functions of the system can be expressed in terms…
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…
We are interested in the harmonic analysis on $p$-adic homogeneous spaces based on spherical functions. In the present paper, we investigate the space $X$ of unitary hermitian matrices of odd size over a ${\mathfrak p}$-adic field of odd…
We compute the leading and sub-leading terms in the asymptotic expansion of the Szeg\"o kernel on the diagonal of a class of pseudoconvex Reinhardt domains whose boundaries are endowed with a general class of smooth measures. We do so by…
We establish the full quasi-Banach range of $L^{p_1}(\mathbb R) \times L^{p_2}(\mathbb R) \rightarrow L^p(\mathbb R)$ bounds for one-dimensional bilinear singular integral operators with homogeneous kernels whose restriction $\Omega$ to the…