Related papers: Notes on Lebesgue integration
The alternative to the replica procedure, which we call the noncommutative replica procedure, is discussed. The detailed comparison with the standard replica procedure is performed.
In this paper, we establish a sequential characterisation of Lebesgue fuzzy metric and explore the relationship between Lebesgue, weak G-complete and compact fuzzy metric spaces. We also discuss the Lebesgue property of several well-known…
We give several algorithms addressing computations of intersections of conjugate subgroups.
We obtain simple proofs of certain inequalites for bivariate means.
Lecture notes as per the title. In the first part, the concepts of a measurable space, measurable maps between measurable spaces and that of a measure on a measurable space are introduced, after which the fundamentals of the theory of…
A finite transformation method is introduced. This method is equivalent to the $Z$ transform method to a certain extent but generalizes it. By applying the presented method to the Bessel functions, it is possible to solve related ordinary…
New index transforms are investigated, which contain as the kernel products of the Bessel and modified Bessel functions. Mapping properties and invertibility in Lebesgue spaces are studied for these operators. Relationships with the…
We consider some applications of the non-homogeneous second order integral equation of Fox. Some new solutions to Fox's integral equation are discussed in relation to number theory.
We introduce the notion of Lebesgue currents. They are a special type of currents involving Lebesgue measure. We apply it to define the intersection of singular cycles, which provides the foundation to the real intersection theory.
This note is the follow up to a paper by M. Waldschmidt.
These informal notes briefly discuss various aspects of Cantor sets.
We improve constants in the Rademacher-Menchov inequality.
We study discretization of Darboux integrable systems. The discretization is done by using $x$- or $y$-integrals of the considered systems. New examples of semi-discrete Darboux integrable systems are obtained.
We study moment rearrangement invariant spaces, which contain as particular cases the generalized Grand Lebesgue Spaces, and provide norm estimates for some operators, not necessarily linear, acting between some measurable rearrangement…
The history of VLBI is summarized with emphasis on the technical aspects. A summary of VLBI systems which are in use is given, and an outlook to the future of VLBI instrumentation.
New index transforms of the Lebedev type are investigated. It involves the real part of the product of the modified Bessel functions as the kernel. The boundedness and invertibility are examined for these operators in the Lebesgue weighted…
Following an idea due to Euler, we evaluate the alternating sums of powers of consrcutive integers.
An approximation result for the bilinear Hilbert transform is proved and used for the inversion of the bilinear Hilbert transform. Also, p-Lebesgue points $(p\geq 1)$ are analyzed.
We study the problem estimation of classical Lebesgue-Riesz and Grand Lebesgue Norm for the fractional integrals and derivatives for the functions from the classical Lebesgue-Riesz spaces as well as from the modified Besov's spaces.
On the base of Lie algebraic and differential geometry methods, a wide class of multidimensional nonlinear integrable systems is obtained, and the integration scheme for such equations is proposed.