相关论文: Notes on Lebesgue integration

In this paper, we present methods to simplify reducible linear differential systems before solving. Classical integrals appear naturally as solutions of such systems. We will illustrate the methods developed in a previous paper on several…

We discuss some aspects of the theory of subelliptic estimates.

The Particle Data Group recommends a set of procedures to be applied when discrepant data are to be combined. We introduce an alternative method based on a more general and solid statistical framework, providing a robust way to include…

We consider the pointwise approximation of a subharmonic function by the logarithm of the modulus of an entire function up to a bounded quantity. In the case of finite order an estimate from below of the planar Lebesgue measure of an…

We study Riemann-Lebesgue integrability of a vector function relative to an arbitrary non-negative set function. We obtain some classical integral properties. Results regarding the continuity properties of the integral and relationships…

Some recent results on evaluating Feynman integrals are reviewed. The status of the method based on Mellin-Barnes representation as a powerful tool to evaluate individual Feynman integrals is characterized. A new method based on Groebner…

We extend in this article the classical imbedding theorems for fractional Lebesgue-Sobolev's spaces into the so-called Grand Lebesgue spaces, with sharp constant evaluation.

The paper develops the method for construction of families of particular solutions to some classes of nonlinear Partial Differential Equations (PDE). Method is based on the specific link between algebraic matrix equations and PDE.…

In this note we prove a class of sharp inequalities for singular integral operators in weighted Lebesgue spaces with angular integrability.

One of the essential questions of the theory of multidimensional integrals concerns the evaluation of integrals taken in given domains. In the simplest case, when integrating over parallelepipeds, evaluation can easily be performed by…

This is a short survey on the recent developments made in the integration theory with effective formulas of algebraic structures stronger or higher than Lie algebras.

These lecture notes highlight the mathematical and computational structure relating to the formulation of, and development of algorithms for, the Bayesian approach to inverse problems in differential equations. This approach is fundamental…

We construct and study certain Liouville integrable, superintegrable, and non-commutative integrable systems, which are associated with multi-sums of products.

We give evaluations in closed form of certain non linear differential equations

These notes present an approach to obtaining monoid operations which are compatible with a given family of mappings in the sense that the mappings become left translations in the monoid. This can be applied to various situations such as the…

In this note we briefly survey and propose some open problems related to isoparametric theory.

This note presents an interesting counterexample to a basic covering problem.

These notes concern linear transformations on R^n and C^n, exponentials of linear transformations, and some related geometric questions.

We survey some results on toric topology.

Some new integrals involving the Stieltjes constants are developed in this paper.