Related papers: Funktionalanalysis Teil I
Formal grammars are extensively used in Computer Science and related fields to study the rules which govern production of a language. The use of these grammars can be extended beyond mere language production. One possibility is to view…
A result is given to find points where a real valued function on the plane is not smooth. Provided this function is induced by a smooth mapping from three dimensions to the plane, from a function on surfaces in three dimensions. This has…
In an abstract Hilbert space setting, we discuss many linear phenomena of mathematical physics. The functional analytic framework presented is used to address continuous dependence of the solution operators $\mathcal{S}(\mathcal{M})$ of…
This article presents a reformulation of the Theory of Functional Connections: a general methodology for functional interpolation that can embed a set of user-specified linear constraints. The reformulation presented in this paper exploits…
How to select variables and identify functional forms for continuous variables is a key concern when creating a multivariable model. Ad hoc 'traditional' approaches to variable selection have been in use for at least 50 years. Similarly,…
With a simple generic approach, we develop a classification that encodes and measures the strength of completeness (or compactness) properties in various types of spaces and ordered structures. The approach also allows us to encode notions…
This work is concerned with the convex analysis of functions defined on (not necessarily finite-dimensional) Hilbert spaces whose values depend solely on a certain ``spectrum'' of the arguments, a class we term ``spectral functions.'' We…
Function is defined as the ensemble of tasks that enable the product to complete the designed purpose. Functional tools, such as functional modeling, offer decision guidance in the early phase of product design, where explicit design…
Classical deep learning typically operates on individual cases. Despite its success, real-world usage often requires repeated inference to estimate statistical quantities for complex decision-making tasks involving uncertainty or…
The Bargmann-Fock space(or Fock space for short) is a fundamental example of reproducing kernel Hilbert spaces that has found fascinating applications across multiple fields of current interest, including quantum mechanics, time-frequency…
Using functional equations, we define functors that generalize standard examples from calculus of one variable. Examples of such functors are discussed and their Taylor towers are computed. We also show that these functors factor through…
We consider functional linear regression models where functional outcomes are associated with scalar predictors by coefficient functions with shape constraints, such as monotonicity and convexity, that apply to sub-domains of interest. To…
A fractal function is a function whose graph is the attractor of an iterated function system. This paper generalizes analytic continuation of an analytic function to continuation of a fractal function.
The variant of calculation of functions of set and their application is offered. In particular: the new measure of system of sets generalizing classical concept of a measure is entered; the variation of set that has allowed to construct a…
In this paper we introduce and investigate a new kind of functional (including ordinary and evolutionary partial) differential equations. The main goal of this paper is to explore our new philosophy by some examples on functional ODEs and…
Lectures notes (in italian) of some arguments of classical analysis, with exercises. A particular emphasis to functional analysis and elementary operator algebra theory is given, by means of exercises and examples.
On the one hand the algebras of linear operators here act on finite-dimensional vector spaces, and on the other hand the point of view is generally an analysts'. Also, one might think of algebras as being used to add more data to basic…
The theory of fractional calculus in the complex plane was not built with a specific application in mind. The main obstacle to application was the difficulty with obtaining analytic continuations of fractional derivatives and integrals. It…
The paper is devoted to a comprehensive second-order study of a remarkable class of convex extended-real-valued functions that is highly important in many aspects of nonlinear and variational analysis, specifically those related to…
Functors with an instance of the Traversable type class can be thought of as data structures which permit a traversal of their elements. This has been made precise by the correspondence between traversable functors and finitary containers…