相关论文: Notes on Lebesgue integration

A short introduction to the mathematical methods and technics of differential algebras and modules adapted to the problems of mathematical and theoretical physics is presented.

Recently proposed procedure of constructing maximally superintegrable systems of Winternitz type is further developed and illustrated by an example of system admitting an explicit construction of angle variables and additional integrals of…

We give a presentation of abelian class field theory.

We make several comments on "Note on the Analytical Solution of the Rabi Model" (arXiv:1210.4946).

We compare various viewpoints on down-sets (simplicial complexes), illustrating how the combinatorial inclusion-exclusion principle may serve as an alternative to more advanced methods of studying their face numbers.

We estimate the Lebesgue constants for Lagrange interpolation processes on one or several intervals by rational functions with fixed poles. We admit that the poles have accumulation points on the intervals. To prove it we use an analog of…

We note an inversion property of the fusion map associated to many semibialgebras.

We construct a non-doubling measure on the real line, all tangent measures of which are equivalent to Lebesgue measure.

An analytical approach to convolution of functions, which appear in perturbative calculations, is discussed. An extended list of integrals is presented.

We describe a method to compute Hurwitz-Hodge integrals.

These informal notes discuss a few basic notions and examples, with emphasis on constructions that may be relevant for analysis on metric spaces.

Various uses of the renormalization group are examined.

The Integration Theory of Linear Ordinary Differential Equation.

This article handles in a short manner a few Laplace transform pairs and some extensions to the basic equations are developed. They can be applied to a wide variety of functions in order to find the Laplace transform or its inverse when…

We introduce a general definition of hybrid transforms for constructible functions. These are integral transforms combining Lebesgue integration and Euler calculus. Lebesgue integration gives access to well-studied kernels and to regularity…

A compendium for outsiders.

In this note, we establish some new results on some special types of function algebras and also give new proofs to some existing ones

We present a few techniques for proving $L^p$ estimates for martingales. Basic applications to It\^o integration and rough paths are included.

The work studies some Difference equations, which are connected with Mejer's function.

Another approach to constructing an upper bound for the Riemann-Farey sum is described.