Related papers: Self-affine spectral measures and frame spectral m…
We show that for Lebesgue almost all $d$-tuples $(\theta_1,\ldots,\theta_d)$, with $|\theta_j|>1$, any self-affine measure for a homogeneous non-degenerate iterated function system $\{Ax+a_j\}_{j=1}^m$ in ${\mathbb R}^d$, where $A^{-1}$ is…
We prove sharp $L^2$ Fourier restriction inequalities for compact, smooth surfaces in $\mathbb{R}^3$ equipped with the affine surface measure or a power thereof. The results are valid for all smooth surfaces and the bounds are uniform for…
The need to Fourier transform data sets with irregular sampling is shared by various domains of science. This is the case for example in astronomy or sismology. Iterative methods have been developed that allow to reach approximate…
This paper presents a simple Fourier-matching method to rigorously study resonance frequencies of a sound-hard slab with a finite number of arbitrarily shaped cylindrical holes of diameter ${\cal O}(h)$ for $h\ll1$. Outside the holes, a…
Understanding the limiting behavior of eigenvalues of random matrices is the central problem of random matrix theory. Classical limit results are known for many models, and there has been significant recent progress in obtaining more…
Obtaining constraints from the largest scales of a galaxy survey is challenging due to the survey mask allowing only partial measurement of large angular modes. This scatters information from the harmonic-space 2-point function away from…
We continue our study of the dynamics of meromorphic mappings with small topological degree on a compact K\"ahler surface $X$. Under general hypotheses we are able to construct a canonical invariant measure which is mixing, does not charge…
We consider the problem of density estimation in the context of multiscale Langevin diffusion processes, where a single-scale homogenized surrogate model can be derived. In particular, our aim is to learn the density of the invariant…
The article provides proofs for the regularity of Dirac eigenfunctions, subject to MIT boundary conditions employed on various types of open sets ranging from smooth ones to convex polygons in two dimensions, as well as on half-space and…
We prove that there exists uncountably many pairwise disjoint open subsets of the Gelfand space of the measure algebra on any locally compact non-discrete abelian group which shows that this space is not separable (in fact, we prove this…
In this article, we develop comprehensive frequency domain methods for estimating and inferring the second-order structure of spatial point processes. The main element here is on utilizing the discrete Fourier transform (DFT) of the point…
In this paper we go over the history of the Fuglede or Spectral Set Conjecture as it has developed over the last 30 years or so. We do not aim to be exhaustive and we do not cover important areas of development such as the results on the…
We give a new fast method for evaluating sprectral approximations of nonlinear polynomial functionals. We prove that the new algorithm is convergent if the functions considered are smooth enough, under a general assumption on the spectral…
We describe the scaling scenery associated to Bernoulli measures supported on separated self-affine sets under the condition that certain projections of the measure are absolutely continuous.
Fourier imaging is an indirect imaging method which records the diffraction pattern of the object scene coherently in the focal plane of the imaging system and reconstructs the image using computational resources. The spatial resolution,…
Spectral functions measured with angle-resolved photoemission spectroscopy (ARPES) provide key insight to elucidate the band structure of materials. Comparison with theory requires computing dynamical one-point functions in some equilibrium…
The problem of imaging extended targets (sources or scatterers) is formulated in the framework of compressed sensing with emphasis on subwavelength resolution. The proposed formulation of the problems of inverse source/scattering is…
We derive new bounds for the condition number of kernel matrices, which we then use to enhance existing non-asymptotic test error bounds for kernel ridgeless regression (KRR) in the over-parameterized regime for a fixed input dimension. For…
In dynamical systems, shrinking target sets and pointwise recurrent sets are two important classes of dynamically defined subsets. In this article we introduce a mild condition on the linear parts of the affine mappings that allow us to…
We develop a unified approach for establishing rates of decay for the Fourier transform of a wide class of dynamically defined measures. Among the key features of the method is the systematic use of the $L^2$-flattening theorem obtained in…