Related papers: A nice example of Lebesgue integration
In this article, we focus on the construction of multivariate fractal functions in Lebesgue spaces along with some properties of associated fractal operator. First, we give a detailed construction of the fractal functions belonging to…
This paper provides a Liouville principle for integration in terms of exponential integrals and incomplete gamma functions.
We utilize a combination of integral transforms, including the Laplace transform, with some classical results in analytic number theory concerning the Riemann $\xi$-function, to obtain a new integral equation. We also provide a new proof of…
A comparison between a set-valued Gould type and simple Birkhoff integrals of $bf(X)$-valued multifunctions with respect to a non-negative set functionis given. Relationships among them and Mc Shane multivalued integrability is given under…
We propose a new class of transforms that we call {\it Lehmer Transform} which is motivated by the {\it Lehmer mean function}. The proposed {\it Lehmer transform} decomposes a function of a sample into their constituting statistical…
We offer a solution to a functional equation using properties of the Mellin transform. A new criteria for the Riemann Hypothesis is offered as an application of our main result, through a functional relationship with the Riemann xi…
An integral representation of the partition function for general $n$-dimensional Ising models with nearest or non-nearest neighbours interactions is given. The representation is used to derive some properties of the partition function. An…
In this paper, we establish several inequalities for different convex mappings that are connected with the Riemann-Liouville fractional integrals. Our results have some relationships with certain integral inequalities in the literature.
Our aim in this report is to investigate the asymptotic behavior of Mittag-Leffler functions. We give some estimates involving the Mittag-Leffler functions and their derivatives.
The Bochner integral is a generalization of the Lebesgue integral, for functions taking their values in a Banach space. Therefore, both its mathematical definition and its formalization in the Coq proof assistant are more challenging as we…
We develop notions of integrable functions within the theory of schemic motivic integration.
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…
We describe some examples of non abelian nilpotent Lie algebras which are not algebraic.
Left and right-continuous functions play an important role in Real analysis, especially in Measure Theory and Integration on the real line and in Stochastic processes indexed by a continuous real time. Semi-continuous functions are also of…
A relationship between the Riemann zeta function and a density on integer sets is explored. Several properties of the examined density are derived.
We present a new proof to a general result due to Kestelman. Our proof differs completely from the other proofs we know and we hope that readers will find it clearer. We also include a quite exhaustive bibliographical analysis on related…
New index transforms with Weber type kernels, consisting of products of Bessel functions of the first and second kind are investigated. Mapping properties and inversion formulas are established for these transforms in Lebesgue spaces. The…
We derive new reduction formulas for the incomplete beta function and the Lerch transcendent in terms of elementary functions. As an application, we calculate some new integrals. Also, we use these reduction formulas to test the performance…
In [22], it was proved that as long as the integrand has certain properties, the corresponding It\^o integral can be written as a (parameterized) Lebesgue integral (or a Bochner integral). In this paper, we show that such a question can be…
We improve the Lieb-Thirring type inequalities by Demuth, Hansmann and Katriel (J. Funct. Anal. 2009) for Schr\"odinger operators with complex-valued potentials. Our result involves a positive, integrable function. We show that in the…