Related papers: Analysis on Lambert-Tsallis functions
The present article is devoted to one example which related to the Salem function. The main attention is given to properties of one type of functions including items related to functional equations, graphs, the Lebesgue integral, etc.
We compute up to a constant factor the Christoffel function on planar domains with boundary consisting of finitely many $C^2$ curves such that each corner point of the boundary has interior angle strictly between $0$ and $\pi$. The…
The Laplace transform of $|\zeta(1/2+it)|$ is investigated, for which a precise expression is obtained, valid in a certain region in the complex plane. The method of proof is based on complex integration and spectral theory of the…
Paper is devoted to extremal problems in geometric function theory of complex variables associated with estimates of functionals defined on the systems of non-overlapping domains. In particular, we strengthen some known result in this…
A fully diagonalized spectral method using generalized Laguerre functions is proposed and analyzed for solving elliptic equations on the half line. We first define the generalized Laguerre functions which are complete and mutually…
We establish sharp inequalities involving the incomplete Beta and Gamma functions. These inequalities arise in the approximation of generalized Bernstein functions by higher order Thorin-Bernstein functions. Furthermore, new properties of a…
We study a new generalized version of the point pair function defined with a constant $\alpha>0$. We prove that this function is a quasi-metric for all values of $\alpha>0$, and compare it to several hyperbolic-type metrics, such as the…
It is shown that the Laurent series of a holomorphic function smooth up to the boundary on a Reinhardt domain in $\mathbb{C}^n$ converges unconditionally to the function in the Fr\'{e}chet topology of the space of functions smooth up to the…
We consider a combination of heavily trimmed sums and sample quantiles which arises when examining properties of clustering criteria and prove limit theorems. The object of interest, which we call the Empirical Cross-over Function, is an…
We investigate the sample path properties of Martin-L\"of random Brownian motion. We show (1) that many classical results which are known to hold almost surely hold for every Martin-L\"of random Brownian path, (2) that the effective…
We study metric and analytic properties of generalized lemniscates E_t(f)={z:ln|f(z)|=t}, where f is an analytic function. Our main result states that the length function |E_t(f)| is a bilateral Laplace transform of a certain positive…
The use of quadratic forms of the empirical process for the two-sample problem in the context of functional data is considered. The convergence of the family of statistics proposed to a Gaussian limit is established under metric entropy…
The squared Laplace operator acting on symmetric rank-two tensor fields is studied on a (flat) Riemannian manifold with smooth boundary. Symmetry of this fourth-order elliptic operator is obtained provided that such tensor fields and their…
We develop a well-defined spectral representation for two-point functions in relativistic Integrable QFT in finite density situations, valid for space-like separations. The resulting integral series is based on the infinite volume, zero…
This paper establishes connections between the boundary behaviour of functions representable as absolutely convergent Dirichlet series in a half-plane and the convergence properties of partial sums of the Dirichlet series on the boundary.…
This article offers a comprehensive treatment of polynomial functional regression, culminating in the establishment of a novel finite sample bound. This bound encompasses various aspects, including general smoothness conditions, capacity…
In the present paper, we introduced the extended bicomplex plane $\bar{\mathbb{T}}$, its geometric model: the bicomplex Riemann sphere, and the bicomplex chordal metric that enables us to talk about the convergence of the sequences of…
In this paper, we provide a new means of establishing solvability of the Dirichlet problem on Lipschitz domains, with measurable data, for second order elliptic, non-symmetric divergence form operators. We show that a certain optimal…
For most values of parameters $\lambda$ and $\alpha$, the zeros of the Lerch zeta-function $L(\lambda, \alpha, s)$ are distributed very chaotically. In this paper we consider the special case of equal parameters $L(\lambda, \lambda, s)$ and…
We find an explicit upper bound for general $L$-functions on the critical line, assuming the Generalized Riemann Hypothesis, and give as illustrative examples its application to some families of $L$-functions and Dedekind zeta functions.…