Related papers: Some Notes on Standard Borel and Related Spaces
We introduce and investigate classes of normed or quasinormed distribution spaces of generalized smoothness that can be obtained by various interpolation methods applied to classical Sobolev, Nikolskii-Besov, and Triebel-Lizorkin spaces. An…
A selection of basic results on Borel reducibility of ideals and equivalence relations, especially those with comparably short proofs. This is an unfinished text as yet. Some proofs have missing parts and loose ends. [email protected] and…
These informal notes, not intended for publication, provide an approach to the Borsuk--Ulam theorem via Stokes' theorem, in a similar spirit to Lima's proof of the Brouwer fixed point theorem. They are intended to be accessible to anyone…
Similar to linear spaces, many examples of quasilinear spaces have a notion of multiplication of the elements. To characterising these examples, in the present paper we generalize the notion of quasilinear spaces and introduce…
The present technical notes offer a brief summary of the essential points of electromagnetism at the undergraduate physics level. Some problems are presented at the end of each section; those with solutions are marked with an asterisk.
The aim of this paper is to provide Markov-type inequalities in the setting of weighted Sobolev spaces when the considered weights are generalized classical weights. Also, as results of independent interest, some basic facts about Sobolev…
This note describes a way of obtaining e that differs from the standard one. It could be used as an alternate way of showing how the value of e is obtained. No attempt is made to show the existence of the limit in the definition of e that…
A basic family of solenoids is discussed, especially from the point of view of analysis on metric spaces.
An exposition of the basic geometry of twistor integrals, intended for mathematicians.
This brief note, written for non-specialists, aims at drawing an introductive overview of the multiverse issue.
These notes aim to give an introduction to a few aspects of noncommutative geometry.
The special case of closed subsets of C^n is briefly discussed.
This article explains the relationship between analytic and algebraic order in case of abstract pseudo-differential operators for a regular spectral triple.
In this brief note the operatorial methods are applied to the study of the Airy function and its generalizations.
These notes, associated with a topics course, are concerned with some general methods related to norms and linear transformations.
These notes concern linear transformations on R^n and C^n, exponentials of linear transformations, and some related geometric questions.
We present a brief introduction to analytic capacity, with an emphasis on its numerical computation. We also discuss several related open problems.
Work in progress concerning alternative formalizations of arithmetic.
This text consists of five relatively systematic notes on Gr\"obner bases and free resolutions of modules over solvable polynomial algebras.
We provide the analytic forms of the distributions for the sum of ordered spacings. We do this both for the case where the boundaries are included in the calculation of the spacings and the case where they are excluded. Both the probability…