Related papers: Spectral Stieltjes-Type Integration and Some Appli…
The non-Archimedean spectral theory and spectral integration is developed. The analog of the Stone theorem is proved. Applications are considered for algebras of operators.
We introduce the concept of Stieltjes integral of an operator-valued function with respect to the spectral measure associated with a normal operator. We give sufficient conditions for the existence of this integral and find bounds on its…
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…
We study the process of integration on time scales in the sense of Riemann-Stieltjes. Analogues of the classical properties are proved for a generic time scale, and examples are given.
For $\mu>\beta>0$, the generalized Stieltjes operators $$ \mathcal{S}_{\beta,\mu} f(t):={t^{\mu-\beta}}\int_0^\infty {s^{\beta-1}\over (s+t)^{\mu}}f(s)ds, \qquad t>0, $$ defined on Sobolev spaces $\mathcal{T}_p^{(\alpha)}(t^\alpha)$ (where…
Integrating with respect to functions which are constant on intervals whose bounds are discontinuity points (of those functions) is frequent in many branches of Mathematics, specially in stochastic processes. For such functions and alike…
Some new integrals involving the Stieltjes constants are developed in this paper.
We study various Stieltjes integrals as Poisson-Stieltjes, conjugate Poisson-Stieltjes, Schwartz-Stieltjes and Cauchy-Stieltjes and prove theorems on the existence of their finite angular limits a.e. in terms of the singular…
The theory of Banach spaces of Dirichlet series has drawn an increasing attention in the recent 25 years. One of the main interest of this new theory is that of defining analogues of the classical spaces of analytic functions on the unit…
Stieltjes integral theorem is more commonly known by the phrase 'integration by parts' and enables rearrangement of an otherwise intractable integral to a more amenable form; often permitting completion of an integral in closed form.…
In this paper several joint spectra for a finite commuting family of closed operators in Banach space are considered, some new relations between these spectra established (earlier only the inclusion of the Taylor spectrum in the commutant…
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.
Inter alia, we present a Fourier series involving the generalised Stieltjes constants.
We prove dynamic inequalities of majorisation type for functions on time scales. The results are obtained using the notion of Riemann-Stieltjes delta integral and give a generalization of [App. Math. Let. 22 (2009), no. 3, 416--421] to time…
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.…
We present a new and simple approach to the theory of multiple operator integrals that applies to unbounded operators affiliated with general von Neumann algebras. For semifinite von Neumann algebras we give applications to the Fr\'echet…
We study the existence of Riemann-Stieltjes integrals of bounded functions against a given integrator. We are also concerned with the possibility of computing the resulting integrals by means of related Riemann integrals. In particular, we…
Sharp inequalitieis of Gruss type for Stieltjes integrals with application in numerical integration are provided.
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…
Some new integrals involving the Stieltjes constants are developed in this paper.