相关论文: Notes on Lebesgue integration

In this note a general approach is suggested for comparison of operators. This is done by means of the Fourier transform of a measure. This approach is applied to comparison of approximation properties of various summability methods of the…

We provide a Liouville principle for integration in terms of elliptic integrals. Our methods are essentially those of Abel and Liouville changed to modern notation. We expose Lie theoretic aspect of Liouville's work.

This paper presents a point-free version of the Lebesgue integral for simple functions on $\sigma$-locales. It describes the integral with respect to a measure defined on the coframe of all $\sigma$-sublocales, moving beyond the constraints…

In this article we investigate the so-called Bilateral Small Lebesgue Spaces: prove that they are associated to the Grand Lebesgue spaces, calculate its fundamental functions and Boyd's indices find its dual spaces etc.

We consider several possible approaches to evaluating an integral involving the digamma function and a related logarithmic series.

This paper provides a Liouville principle for integration in terms of dilogarithm and partial result for polylogarithm.

In this paper a new general approach is developed to construct and study Lebesgue type decompositions of linear operators $T$ in the Hilbert space setting. The new approach allows to introduce an essentially wider class of Lebesgue type…

A survey of work on motivic integration.

Fundamentals on Lie group methods and applications to differential equations are surveyed. Many examples are included to elucidate their extensive applicability for analytically solving both ordinary and partial differential equations.

In this note we refine the alternativity in some bifurcation theorems of Rabinowitz type, and then improve a few of results in Lu (2022) [17].

We present some informal remarks on aspects of relativistic quantum computing.

These notes give an elementary approach to parts of the theory of standard Borel and analytic spaces.

This note gives a simple approach to q-analogues of some results associated with Abel polynomials.

The purpose of this note is to compare various approximation methods as applied to the inverse of the Bessel function of the first kind, in a given domain of the complex plane.

We give a gentle introduction to Frobenius splittings. Then we recall a few results that have been obtained with the method.

We present the statistical approach to the combining of signal significances.

Computability theory is used to evaluate the complexity of classifying various kinds of Lebesgue spaces and associated isometric isomorphism problems.

We present some new lower bound estimates for certain numbers in Laver table theory and introduce several related structures of interest.

These informal notes deal with a number of questions related to sums and integrals in analysis.

Using a new result on the integral involving the product of Bessel functions and associated Laguerre polynomials, published in the mathematical literature some time ago, we present an alternative method for calculating discrete-discrete…