Related papers: Generalized Functions in Infinite Dimensional Anal…
We establish Gaussian limits for general measures induced by binomial and Poisson point processes in d-dimensional space. The limiting Gaussian field has a covariance functional which depends on the density of the point process. The general…
Gaussian process is a theoretically appealing model for nonparametric analysis, but its computational cumbersomeness hinders its use in large scale and the existing reduced-rank solutions are usually heuristic. In this work, we propose a…
Non-linear gravitational collapse introduces non-Gaussian statistics into the matter fields of the late Universe. As the large-scale structure is the target of current and future observational campaigns, one would ideally like to have the…
A discussion of methods of nonisotropic fine quantitative complex analysis on lineally convex domains of finite type is given. The needed support functions with best possible estimates are considered together with the estimation of their…
We find an infinite number of noncommutative geometries which posses a differential structure. They generalize the two dimensional noncommutative plane, and have infinite dimensional representations. Upon applying generalized coherent…
Co lombeau's construction of generalized functions (in its special variant) is extended to a theory of generalized sections of vector bundles. As particular cases, generalized tensor analysis and exterior algebra are studied. A point value…
We establish a generic formula for the generalised q-dimensions of measures supported by almost self-affine sets, for all q>1. These q-dimensions may exhibit phase transitions as q varies. We first consider general measures and then…
We develop a framework for generalized variational inference in infinite-dimensional function spaces and use it to construct a method termed Gaussian Wasserstein inference (GWI). GWI leverages the Wasserstein distance between Gaussian…
Functional graphical models have undergone extensive development during the recent years, leading to a variety models such as the functional Gaussian graphical model, the functional copula Gaussian graphical model, the functional Bayesian…
Based on the matrix expression of general nonlinear numerical analogues presented by the present author, this paper proposes a novel philosophy of nonlinear computation and analysis. The nonlinear problems are considered an ill-posed linear…
Multi-dimensional functional data arises in numerous modern scientific experimental and observational studies. In this paper we focus on longitudinal functional data, a structured form of multidimensional functional data. Operating within a…
We propose in this short note a prime numbers-based method for constructing probability measures on infinite-dimensional Banach spaces annihilating all finite-dimensional subspaces, supplementing the methods of construction of Gaussian…
We present an extension of the methods of classical Lie group analysis of differential equations to equations involving generalized functions (in particular: distributions). A suitable framework for such a generalization is provided by…
We investigate ergodic theory of Poisson suspensions. In the process, we establish close connections between finite and infinite measure preserving ergodic theory. Poisson suspensions thus provide a new approach to infinite measure…
We present an approach for construction of functional bases of differential invariants for some infinite-dimensional algebras with coefficients of generating operators depending on arbitrary functions. An example for the…
We introduce a particular nonlinear generalization of quantum mechanics which has the property that it is exactly solvable in terms of the eigenvalues and eigenfunctions of the Hamiltonian of the usual linear quantum mechanics problem. We…
We present a multifractal formalism for measures on infinite dimensional metric spaces, in terms of scales instead of dimensions in the classical multifractal analysis. We prove a multifractal formalism with a suitable scaling, called…
We present a common ground for infinite sums, unordered sums, Riemann/Lebesgue integrals, arc length and some generalized means. It is based on extending functions on finite sets using Hausdorff metric in a natural way.
These lecture notes contain an introduction to some of the fundamental ideas and results in analysis and probability on infinite-dimensional spaces, mainly Gaussian measures on Banach spaces. They originated as the notes for a topics course…
The article is devoted to approximate, global and along curves differentiability of functions over non-archimedean infinite fields with non-trivial valuations. Fields with zero and non-zero characteristics are considered. Spaces of…