Related papers: Funktionalanalysis Teil I
This is a tutorial introduction to the functional analysis mathematics needed in many physical problems, such as in waves in continuous media. Functional analysis takes us beyond finite matrices, allowing us to work with infinite sets of…
The aim of this paper is to present a survey of some recent results obtained in the study of spaces with asymmetric norm. The presentation follows the ideas from the theory of normed spaces (topology, continuous linear operators, continuous…
As high-dimensional and high-frequency data are being collected on a large scale, the development of new statistical models is being pushed forward. Functional data analysis provides the required statistical methods to deal with large-scale…
Dimensional analysis provides many simple and useful tools for various situations in science. The objective of this paper is to investigate its relations to functions, i.e., the dimensions for functions that yield physical quantities and…
Functional data analysis is typically conducted within the $L^2$-Hilbert space framework. There is by now a fully developed statistical toolbox allowing for the principled application of the functional data machinery to real-world problems,…
Functionals are an important research subject in Mathematics and Computer Science as well as a challenge in Information Technologies where the current programming paradigm states that only symbolic computations are possible on higher order…
This book concentrates on functional analysis. The text is written so that it can be followed on the basis of high school mathematics. The book introduces the set theoretical foundations of mathematics, the basic theories of linear algebra…
Over the decades, Functional Analysis has been enriched and inspired on account of demands from neighboring fields, within mathematics, harmonic analysis (wavelets and signal processing), numerical analysis (finite element methods,…
These informal notes are concerned with spaces of functions in various situations, including continuous functions on topological spaces, holomorphic functions of one or more complex variables, and so on.
Functional data that are nonnegative and have a constrained integral can be considered as samples of one-dimensional density functions. Such data are ubiquitous. Due to the inherent constraints, densities do not live in a vector space and,…
Functionals (i.e. functions of functions) are widely used in quantum field theory and solid-state physics. In this paper, functionals are given a rigorous mathematical framework and their main properties are described. The choice of the…
Function (linear) spaces on which an arbitrary function operates (i.e. the space is stable w.r.t. the pointwise unary operation defined by the function) were investigated, for continuous real or complex operations, by deLeeuw-Katznelson,…
Functional data analysis (FDA) is a statistical framework that allows for the analysis of curves, images, or functions on higher dimensional domains. The goals of FDA, such as descriptive analyses, classification, and regression, are…
Despite of various similar features, Functional Data Analysis and High-Dimensional Data Analysis are two major fields in Statistics that grew up recently almost independently one from each other. The aim of this paper is to propose a survey…
The work is devoted to the construction of a new type of intervals -- functional intervals. These intervals are built on the idea of expanding boundaries from numbers to functions. Functional intervals have shown themselves to be promising…
This note tries to show that a re-examination of a first course in analysis, using the more sophisticated tools and approaches obtained in later stages, can be a real fun for experts, advanced students, etc. We start by going to the…
Functional principal components (FPC's) provide the most important and most extensively used tool for dimension reduction and inference for functional data. The selection of the number, d, of the FPC's to be used in a specific procedure has…
A natural connection between rational functions of several real or complex variables, and subspace collections is explored. A new class of function, superfunctions, are introduced which are the counterpart to functions at the level of…
We introduce vectorial and topological continuities for functions defined on vector metric spaces and illustrate spaces of such functions. Also, we describe some fundamental classes of vector valued functions and extension theorems.
Inspired by the theories of Kaplansky-Hilbert modules and probability theory in vector lattices, we generalise functional analysis by replacing the scalars $\mathbb{R}$ or $\mathbb{C}$ by a real or complex Dedekind complete unital…