相关论文: Spectral Stieltjes-Type Integration and Some Appli…
In this paper holomorphic families of linear relations which belong to the Stieltjes or inverse Stieltjes class are studied. It is shown that in their domain of holomorphy ${\mathbb C}\setminus{\mathbb R}_+$ the values of Stieltjes and…
In the present paper we prove a Stieltjes type theorem on the convergence of a sequence of rational functions associated with a mixed type Hermite-Pad\'e approximation problem of a Nikishin system of functions and analyze the ratio…
In this work, we extend the concept of the Stieltjes derivative to encompass left-continuous derivators with bounded variation, thereby relaxing the monotonicity constraint. This generalization necessitates a refined definition of the…
In the existing works, stochastic sets $\mathbb{B}$ of interval type, along with $\mathbb{B}$-stochastic processes, were introduced within the framework of stochastic analysis. In this paper, we undertake the construction of…
In this paper, motivated by physical considerations, we introduce the notion of modified Riemann sums of Riemann-Stieltjes integrable functions, show that they converge, and compute them explicitely under various assumptions.
Category and multicategory theory provide abstract frameworks for describing structures and their compositions, with multicategories extending traditional categories to handle multi-input operations. These theories enable modular reasoning…
This work will be centered in commutative Banach subalgebras of the algebra of bounded linear operators defined on a Free Banach spaces of countable type. The main goal of this work wil be to formulate a representation theorem for these…
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…
The Stieltjes constants \gamma_k(a) appear as the coefficients in the regular part of the Laurent expansion of the Hurwitz zeta function \zeta(s,a) about s=1. We present series representations of these constants of interest to theoretical…
We offer some comments on series involving the M$\ddot{o}$bius function which approximate sums over primes. To accomplish this, we utilize the derivative of the Gram series by applying Riemann-Stieltjes integration. We offer a new formula…
Classical spectral theory gives a complete description of a single normal operator, but it fails for noncommuting operators, where no canonical joint spectrum or simultaneous diagonalization exists. Existing approaches provide only partial…
We are studying here a family of probability density functions indexed by a real parameter, and constructed from homographic relations between associated Stieltjes transforms. From the analysis of orthogonal polynomials we deduce a family…
Recently, it was conjectured that the first generalized Stieltjes constant at rational argument may be always expressed by means of Euler's constant, the first Stieltjes constant, the $\Gamma$-function at rational argument(s) and some…
This paper is devoted to characterizing the Riemann-Stieltjes operators and pointwise multipliers acting on M${\rm \ddot{o}}$bius invariant spaces $Q_p$, which unify BMOA and Bloch space in the scale of $p$. The boundedness and compactness…
We introduce a class of (tuples of commuting) unbounded operators on a Banach space, admitting smooth functional calculi, that contains all operators of Helffer-Sj\"ostrand type and is closed under the action of smooth proper mappings.…
A closed form of the multi-peakon solutions of the Camassa-Holm equation is found using a theorem of Stieltjes on continued fractions. An explicit formula is obtained for the scattering shifts.
We show that the higher derivatives of the Riemann zeta function may be expressed in terms of integrals involving the digamma function. Related integrals for the Stieltjes constants are also shown. We also present a formula for the…
We describe the proper closed invariant subspaces of the integration operator when it acts continuously on countable intersections and countable unions of weighted Banach spaces of holomorphic functions on the unit disc or the complex…
In this note, we show that the spectral theorem, has two representations; the Stone-von Neumann representation and one based on the polar decomposition of linear operators, which we call the deformed representation. The deformed…
In this work we establish a Stokes-type integral equality for scalarly essentially integrable forms on an orientable smooth manifold with values in the locally convex linear space $\langle B(G),\sigma(B(G),\mathcal{N})\rangle$, where $G$ is…