Related papers: Interpolation and Sampling in Analytic Tent Spaces
We first present an abstract principle for the interchange of infimization and integration over spaces of mappings taking values in topological spaces. New conditions on the underlying space and the integrand are then introduced to convert…
This work investigates theoretically the interplay between interpolation and aggregation in regression. We establish that the $\gamma$-graph dimension characterizes learnability for a broad class of natural aggregation procedures.…
We give a complete description of Riesz bases of reproducing kernels in small Fock spaces. This characterization is in the spirit of the well known Kadets--Ingham 1/4 theorem for Paley--Wiener spaces. Contrarily to the situation in…
Recently, the extrapolation theory has become a mainsteam method to investigate some integral type operators, since it does not depend on the density of spaces. The purpose of this paper is threefold. The first is to establish product…
We propose Splinter, a new technique for proving properties of heap-manipulating programs that marries (1) a new separation logic-based analysis for heap reasoning with (2) an interpolation-based technique for refining heap-shape invariants…
We are interested in comparing probability distributions defined on Riemannian manifold. The traditional approach to study a distribution relies on locating its mean point and finding the dispersion about that point. On a general manifold…
We recently introduced the Fast Newton Transform (FNT), an hierarchical algorithm for performing multivariate Newton interpolation in arbitrary downward closed polynomial spaces of spatial dimension $m$. Here, we analyze the FNT in the…
Topological techniques have become a popular tool for studying information flows in neural networks. In particular, simplicial homology theory is used to analyze how cognitive representations of space emerge from large conglomerates of…
The traditional approach to the quantitative study of segregation is to employ indices that are selected by ``desirable properties''. Here, we detail how information theory underpins entropy-based indices and demonstrate how desirable…
Consider an n by n matrix x_ij, and consider the quantity || x_{i,pi(i)} ||_X where X is a symmetric sequence space as a random variable where the permutation pi is chosen randomly. This was considered by Kwapien and Schutt, and we extend…
We present Nonstandard Analysis by three axioms: the {\em Extension, Transfer and Saturation Principles} in the framework of the superstructure of a given infinite set. We also present several applications of this axiomatic approach to…
Represented spaces form the general setting for the study of computability derived from Turing machines. As such, they are the basic entities for endeavors such as computable analysis or computable measure theory. The theory of represented…
We give a characterization of complete interpolating sequences for the Fock spaces $\mathcal{F}^p_\varphi,\ 1\leq p<\infty$, where $\varphi(z)=\alpha\left(\log^+|z|\right)^2,\ \alpha>0$. Our results are {analogous} to the classical…
We study statistical inference on unit roots and cointegration for time series in a Hilbert space. We develop statistical inference on the number of common stochastic trends embedded in the time series, i.e., the dimension of the…
A function which is analytic and bounded in the Unit disk is called a generator for the Hardy space or the Bergman space if polynomials in that function are dense in the corresponding space. We characterize generators in terms of sub-spaces…
For $\alpha>-1$ and $0<p<\infty$, we study weighted Bergman spaces $\mathcal B^p_\alpha$ of harmonic functions on the real hyperbolic ball and obtain an atomic decomposition of these spaces in terms of reproducing kernels. We show that an…
We introduce a concept for random tilings which, comprising the conventional one, is also applicable to tiling ensembles without height representation. In particular, we focus on the random tiling entropy as a function of the tile…
In this paper, we present a new deep learning architecture for addressing the problem of supervised learning with sparse and irregularly sampled multivariate time series. The architecture is based on the use of a semi-parametric…
The transference theory for Lp spaces of Calderon, Coifman, and Weiss is a powerful tool with many applications to singular integrals, ergodic theory, and spectral theory of operators. Transference methods afford a unified approach to many…
The method of compatible sequences is introduced in order to produce non-trivial (closed) invariant subspaces of (bounded linear) operators. Also a topological tool is used which is new in the search of invariant subspaces: the extraction…