Related papers: Regulated functions. *-integral
Stieltjes boundary problems generalize the customary class of well-posed two-point boundary value problems in three independent directions, regarding the specification of the boundary conditions: (1) They allow more than two evaluation…
Finite-part integration is a recently introduced method of evaluating convergent integrals by means of the finite part of divergent integrals [E.A. Galapon, {\it Proc. R. Soc. A 473, 20160567} (2017)]. Current application of the method…
A series of physically motivated operations appearing in the study of composite materials are interpreted in terms of elementary continued fraction transforms of matrix valued, rational Stieltjes functions.
By using Cauchy integral formula in the theory of complex functions, the authors establish some integral representations for the principal branches of several complex functions involving the logarithmic function, find some properties, such…
We establish bounds for the covariance of a large class of functions of infinite variance stable random variables, including unbounded functions such as the power function and the logarithm. These bounds involve measures of dependence…
Integration at a point is a new kind of integration derived from integration over an interval in infinitesimal and infinity domains which are spaces larger than the reals. Consider a continuous monotonic divergent function that is…
In this paper we present some applications of the Stieltjes constants including, for example, new derivations of Binet's formulae for the log gamma function and the evaluation of some integrals related to the Barnes multiple gamma…
In this work we develop a theory of Stieltjes-analytic functions. We first define the Stieltjes monomials and polynomials and we study them exhaustively. Then, we introduce the Stieltjes analytic functions locally, as an infinite series of…
Let X be a non-empty set and U a ring of subsets of X. The countable additive functions U->{0,1} are called measures. The paper gives some definitions (derivable measures, the Lebesgue-Stieltjes measures) and properties of these functions,…
The paper constitutes the second part on the subject of finite part integration of the generalized Stieltjes transform $S_{\lambda}[f]=\int_0^{\infty} f(x) (\omega+x)^{-\lambda}\mathrm{d}x$ about $\omega = 0$ where now $\lambda$ is a…
In analogy with the Fourier-Stieltjes algebra of a group, we associate to a unital discrete twisted C*-dynamical system a Banach algebra whose elements are coefficients of equivariants representations of the system. Building upon our…
A class of scalar Stieltjes like functions is realized as linear-fractional transformations of transfer functions of conservative systems based on a Schr\"odinger operator T_h in $L_2[a,+\infty)$ with a non-selfadjoint boundary condition.…
In this work we study Stieltjes differential systems of which the derivators are allowed to change sign. This leads to the definition of the notion of \emph{function of controlled variation}, a characterization of precompact sets of…
Using the notion of the truncated variation we obtain a new theorem on the existence and estimation of the Riemann-Stieltjes integral. As a special case of this theorem we obtain an improved version of the Lo\'{e}ve-Young inequality for the…
This book is based on notes compiled over the many years I have been teaching the course "Applied Functional Analysis" in the first year of the Master programme at Delft University of Technology, for students with previous exposure to the…
We continue the study on Kurzweil--Stieltjes integration on compact lines initiated in [doi:10.1007/s11117-025-01161-9]. Given a real valued function $G$ on a compact line, the presented integral is called the Kurzweil--Stieltjes integral…
We define two versions of compositions of matrix-valued rational functions of appropriate sizes and whenever analytic at infinity, offer a set of formulas for the corresponding state-space realization, in terms of the realizations of the…
In this note, we recall Kummer's Fourier series expansion of the 1-periodic function that coincides with the logarithm of the Gamma function on the unit interval $(0,1)$, and we use it to find closed forms for some numerical series related…
We characterise slice-regularity of functions over a real alternative *-algebra using operators that arise in Dunkl operator theory. We present a unifying perspective on hypercomplex analysis by defining a family of function spaces in the…
The concept of Riemann-Stieltjes integral $\int_a^b {f\left( t \right)du\left( t \right)}$; where $f$ is called the integrand, $u$ is called the integrator, plays an important role in Mathematics. The approximation problem of the…