Related papers: Bilateral Operators for Functional Maps
For finding the numerical solution of operator equations in many applications a decomposition in subspaces is needed. Therefore, it is necessary to extend the known method of matrix representation to the utilization of fusion frames. In…
We make use of the Bergman kernel function to study quadrature domains for square-integrable holomorphic functions of several variables. Emphasis is given to generalizing biholomorphic mapping properties of planar quadrature domains to the…
The characterization of a binary function by partial frequency information is considered. We show that it is possible to reconstruct binary signals from incomplete frequency measurements via the solution of a simple linear optimization…
We establish common fixed point theorems for two pairs of weakly compatible self-mappings using an auxiliary function of two variables. Unlike classical results, our theorems do not assume continuity of the mappings and require completeness…
We employ kernel-based approaches that use samples from a probability distribution to approximate a Kolmogorov operator on a manifold. The self-tuning variable-bandwidth kernel method [Berry & Harlim, Appl. Comput. Harmon. Anal.,…
We introduce an exact reformulation of a broad class of neighborhood filters, among which the bilateral filters, in terms of two functional rearrangements: the decreasing and the relative rearrangements. Independently of the image spatial…
We obtain an explicit classification of all $2\times 2$ real hypergeometric Bochner pairs, ie. pairs $(W(x),\mathfrak{D})$ consisting of a $2\times 2$ real hypergeometric differential operator $\mathfrak{D}$ and a $2\times 2$ weight matrix…
In this work, we present a novel non-rigid shape matching framework based on multi-resolution functional maps with spectral attention. Existing functional map learning methods all rely on the critical choice of the spectral resolution…
In this paper, we study solution operators of physical field equations on geometric meshes from a function-space perspective. We reveal that Hodge orthogonality fundamentally resolves spectral interference by isolating unlearnable…
We propose a data-driven framework to learn interaction kernels in stochastic multi-agent systems. Our approach aims at identifying the functional form of nonlocal interaction and diffusion terms directly from trajectory data, without any a…
This paper introduces the concept of functional current as a mathematical framework to represent and treat functional shapes, i.e. sub-manifold supported signals. It is motivated by the growing occurrence, in medical imaging and…
Neural operators have emerged as a powerful tool for solving partial differential equations (PDEs) and other complex scientific computing tasks. However, the performance of single operator block is often limited, thus often requiring…
We introduce \emph{ReMatching}, a novel shape correspondence solution based on the functional maps framework. Our method, by exploiting a new and appropriate \emph{re}-meshing paradigm, can target shape-\emph{matching} tasks even on meshes…
We present some general theorems about operator algebras that are algebras of functions on sets, including theories of local algebras, residually finite dimensional operator algebras and algebras that can be represented as the scalar…
Biharmonic and conformal-biharmonic maps are two fourth-order generalizations of the well-studied notion of harmonic maps in Riemannian geometry. In this article we consider maps into the Euclidean sphere and investigate a geometric…
A finite dimensional operator that commutes with some symmetry group admits quotient operators, which are determined by the choice of associated representation. Taking the quotient isolates the part of the spectrum supporting the chosen…
Regarding quaternions as normal matrices, we first characterize the $2\times 2$ matrix-valued functions, defined on subsets of quaternions, whose values are quaternions. Then we investigate the regularity of quaternionic-valued functions,…
Reproducing kernel Hilbert spaces (RKHSs) are key elements of many non-parametric tools successfully used in signal processing, statistics, and machine learning. In this work, we aim to address three issues of the classical RKHS based…
A common problem in econometrics, statistics, and machine learning is to estimate and make inference on functions that satisfy shape restrictions. For example, distribution functions are nondecreasing and range between zero and one, height…
Persistent homology has become an important tool for extracting geometric and topological features from data, whose multi-scale features are summarized in a persistence diagram. From a statistical perspective, however, persistence diagrams…