For a unital foundation topological *-semigroup S whose representations separate points of S, we show that the spectrum of the Fourier-Stieltjes algebra B(S) is a compact semitopological semigroup. We also calculate B(S) for several examples of S.

The Stieltjes constants γk(a) appear as the coefficients in the regular part of the Laurent expansion of the Hurwitz zeta function ζ(s, a) about s = 1. We present series representations of these constants of interest to theoretical and computational analytic number theory. A particular result gives an addition formula for the Stieltjes constants. As a byproduct, expressions for derivatives of a...

In a note at the end of his paper Recherches sur les fractions continues, Stieltjes gave a necessary and sufficient condition when a continued fraction is represented by a meromorphic function. This result is related to the study of compact Jacobi matrices. We indicate how this notion was developped and used since Stieltjes, with special attention to the results by M.G. Krein. We also pay atten...

Continuous-time quantum walk (CTQW) on a given graph is investigated by using the techniques of the spectral analysis and inverse Laplace transform of the Stieltjes function (Stieltjes transform of the spectral distribution) associated with the graph. It is shown that, the probability amplitude of observing the CTQW at a given site at time t is related to the inverse Laplace transformation of t...

In this paper, we study the irregular growth of an entire function defined by the Laplace-Stieltjes transform of finite order convergent in the whole complex plane and obtain some results about λ-lower type. In addition, we also investigate the problem on the error in approximating entire functions defined by the Laplace-Stieltjes transforms. Some results about the irregular growth, the error, ...

Recently Chen-Liang-Wang (Linear Algebra Appl. 471 (2015) 383–393) present some sufficient conditions for the total positivity of Catalan-Stieltjes matrices. Our aim is to provide a combinatorial interpretation of their sufficient conditions. More precisely, for any Catalan-Stieltjes matrix A we construct a digraph with a weight, which is positive under their sufficient conditions, such that ev...

Volterra-Stieltjes integral equations have been studied in the space of continuous functions in many papers for example, (see [3]-[7]). Our aim here is to studing the existence of weak solutions to a nonlinear integral equation of Volterra-Stieltjes type in a reflexive Banach space. A special case will be considered.

Stieltjes’ work on continued fractions and the orthogonal polynomials related to continued fraction expansions is summarized and an attempt is made to describe the influence of Stieltjes’ ideas and work in research done after his death, with an emphasis on the theory of orthogonal polynomials.

In this paper we use the resolvent semigroup associated to a C0semigroup to introduce the vector-valued Stieltjes transform defined by a C0-semigroup. We give new results which extend known ones in the case of scalar generalized Stieltjes transform. We work with the vector-valued Weyl fractional calculus to present a deep connection between both concepts. Mathematics Subject Classification (200...

Starting from a strong Stieltjes distribution φ, general sequences of orthogonal Laurent polynomials are introduced and some of their most relevant algebraic properties are studied. From this perspective, the connection between certain quadrature formulas associated with the distribution φ and two-point Padé approximants to the Stieltjes transform of φ is revisited. Finally, illustrative numeri...