Related papers: A Short Course on Frame Theory

We survey current developments in the approximation theory of sequence modelling in machine learning. Particular emphasis is placed on classifying existing results for various model architectures through the lens of classical approximation…

In this article, we define the notion of a filtration and then give the basic theorems on initial and progressive enlargements of filtrations.

We provide a short proof of the 1-dimensional flat chain conjecture.

In this paper we will look at the connection of frames and finite dimensionality. A main focus is to present simple algorithms and make them available online. The main result is a way to 'switch' between different frames, giving an…

The paper contains a review on the general connection theory on differentiable fibre bundles. Particular attention is paid to (linear) connections on vector bundles. The (local) representations of connections in frames adapted to holonomic…

This article gives a brief survey of the theory and applications of anomalies.

A short survey about combinatorics on words and algorithmic methods in a ring. Special attention is given to Shirshov's results. Adopted for undegraduate students.

These notes on string theory are based on a series of talks I gave during my graduate studies. As the talks, this introductory essay is intended for young students and non-string theory physicists.

We give an elementary proof to Hasse theorem.

A general theory of programs, programming and programming languages built up from a few concepts of elementary set theory. Derives, as theorems, properties treated as axioms by classic approaches to programming. Covers sequential and…

We study approximations of theories both in general context and with respect to some natural classes of theories. Some kinds of approximations are considered, connections with finitely axiomatizable theories and minimal generating sets of…

We survey the classical results of the Dirichlet Approximation Theorem.

This is a survey of the spectral theory of tensors.

An algebraic deformation theory of coalgebra morphisms is constructed.

A very short proof of the Fej\'er-Riesz lemma is presented in the matrix case

This is a reference volume on polyfold and Fredholm theory.

A De Rham model for string topology based on the theory of iterated integrals is presented.

\emph{A root frame} for $\mathbb{R}^d$ is a finite frame whose vectors form a root system. In this note we establish some elementary properties of this class of frames and prove that root frames constitute a subclass of scalable frames. In…

This article gives a foundational account of various characterizations of framed links in the $3$-sphere.

A simple, though rarely considered, thought experiment on relativistic rotation is described in which internal inconsistencies in the theory of relativity seem to arise. These apparent inconsistencies are resolved by appropriate insight…