Paley-Wiener description of K-spherical Besov spaces on the Heisenberg group

Frames for spaces of Paley-Wiener functions on Riemannian manifolds

It is shown that Paley-Wiener functions on Riemannian manifolds of bounded geometry can be reconstructed in a stable way from some countable sets of their inner products with certain distributions of compact support. A reconstruction method in terms of frames is given which is a generalization of the classical result of Duffin-Schaeffer about exponential frames on intervals. All results are specified in the case of the two-dimensional hyperbolic space in its Poincare upper half-plane realization.

Paley-Wiener 典范系统的直接谱问题

Direct spectral problems for Paley-Wiener canonical systems

本文研究半直线上典范Hamiltonian系统的直接谱问题，通过反转逆问题算法求解阶梯函数Hamiltonian，并利用阶梯函数逼近证明非阶梯函数Hamiltonian的谱测度收敛性。

Homogeneous Besov spaces on stratified Lie groups and their wavelet characterization

We establish wavelet characterizations of homogeneous Besov spaces on stratified Lie groups, both in terms of continuous and discrete wavelet systems. We first introduce a notion of homogeneous Besov space $\dot{B}_{p,q}^s$ in terms of a Littlewood-Paley-type decomposition, in analogy to the well-known characterization of the Euclidean case. Such decompositions can be defined via the spectral measure of a suitably chosen sub-Laplacian. We prove that the scale of Besov spaces is independent of the precise choice of Littlewood-Paley decomposition. In particular, different sub-Laplacians yield th…

A Discrete Helgason-Fourier transform for Sobolev and Besov functions on noncompact symmetric spaces

Let $f$ be a Paley-Wiener function in the space $L_{2}(X)$, where $X$ is a symmetric space of noncompact type. It is shown that by using the values of $f$ on a sufficiently dense and separated set of points of $X$ one can give an exact formula for the Helgason-Fourier transform of $f$. In order to find a discrete approximation to the Helgason-Fourier transform of a function from a Besov space on $X$ we develop an approximation theory by Paley-Wiener functions in $L_{2}(X)$.

Besov spaces for Schrodinger operators with barrier potentials

Let H be a Schrodinger operator with barrier potential on the real line. We define the Besov spaces for H by developing the associated Littlewood-Paley theory. This theory depends on the decay estimates of the spectral operator in the high and low energies. We also prove a Mikhlin-Hormander type multiplier theorem on these spaces, including the Lp boundedness result. Our approach has potential applications to other Schrodinger operators with short-range potentials, as well as in higher dimensions.

Paley-Littlewood decomposition for sectorial operators and interpolation spaces

We prove Paley-Littlewood decompositions for the scales of fractional powers of $0$-sectorial operators $A$ on a Banach space which correspond to Triebel-Lizorkin spaces and the scale of Besov spaces if $A$ is the classical Laplace operator on $L^p(\mathbb{R}^n).$We use the $H^\infty$-calculus, spectral multiplier theorems and generalized square functions on Banach spaces and apply our results to Laplace-type operators on manifolds and graphs, Schrödinger operators and Hermite expansion.We also give variants of these results for bisectorial operators and for generators of groups with a bounded…