One can slightly modify the usual L, differentiability constraints of Sobolev types on densities
with the help of Besov norms. This has the advantage, using the wavelets characterization of …

Gaussian processes are used in many machine learning applications that rely on
uncertainty quantification. Recently, computational tools for working with these models in …

Classical and nonclassical Besov and Triebel-Lizorkin spaces with complete range of
indices are developed in the general setting of Dirichlet space with a doubling measure and …

Let X be a space of homogeneous type and L be a nonnegative self-adjoint operator on L2
(X) satisfying Gaussian upper bounds on its heat kernels. In this paper, we develop the …

We introduce heat semigroup-based Besov classes in the general framework of Dirichlet
spaces. General properties of those classes are studied and quantitative regularization …

One of the most influential contributions of Frazier and Jawerth is the construction of the
discrete decomposition transformation, the so-called &-transform, on spaces of distributions …

Convergence of the Bayes posterior measure is considered in canonical statistical settings
where observations sit on a geometrical object such as a compact manifold, or more …

We prove necessary density conditions for sampling in spectral subspaces of a second-
order uniformly elliptic differential operator on ℝ d with slowly oscillating symbol. For …

Abstract Homogeneous Besov and Triebel–Lizorkin spaces with complete set of indices are
introduced in the general setting of a doubling metric measure space in the presence of a …

We introduce a novel harmonic analysis for functions defined on the vertices of a strongly
connected directed graph (digraph) of which the random walk operator is the cornerstone …