Related papers: An integral representation for Herglotz-Nevanlinna…
The integral representation of the two-parameter Mittag-Leffler function $E_{\rho,\mu}(z)$ is considered in the paper that expresses its value in terms of the contour integral. For this integral representation, the transition is made from…
An integral representation result is obtained for the relaxation of a class of energy functionals depend- ing on two vector fields with different behaviors, which may appear in the context of image decomposition and thermochemical…
In this paper, we mainly propose improvements of the logarithmic difference lemma for meromorphic functions in several complex variables, and then investigate meromorphic solutions of partial difference equations from the viewpoint of…
A two-parameter characteristic of functions meromorphic on annuli is introduced and an extension of the Nevanlinna value distribution theory for such functions is proposed.
In this paper we investigate a class of integrals that were encountered in the course of a work on statistical plasma physics, in the so-called Sommerfeld temperature-expansion of the electronic entropy. We show that such integrals,…
We investigate subclasses of generalized Bernstein functions related to complete Bernstein and Thorin-Bernstein functions. Representations in terms of incomplete beta and gamma as well as hypergeometric functions are presented. Several…
In this note we review some recent results concerning integral representation properties of local functionals driven by Lipschitz continuous anisotropies.
For an inner function $\theta$ with $\theta'\in\mathcal N$, where $\mathcal N$ is the Nevanlinna class, several problems are posed in connection with the canonical (inner-outer) factorization of $\theta'$.
Integral representation results are obtained for the relaxation of some classes of energy functionals depending on two vector fields with different behaviors, which may appear in the context of image decomposition and thermochemical…
In this paper, we study a class of Borel measures on $\mathbb{R}^n$ that arises as the class of representing measures of Herglotz-Nevanlinna functions. In particular, we study product measures within this class where products with the…
We consider a two-spectra inverse problem for the one-dimensional Schr\"{o}dinger equation with boundary conditions containing rational Herglotz--Nevanlinna functions of the eigenvalue parameter and provide a complete solution of this…
Maximon has recently given an excellent summary of the properties of the Euler dilogarithm function and the frequently used generalizations of the dilogarithm, the most important among them being the polylogarithm function $Li_(z)$. The…
The aim of this note is to prove a representation theorem for left--invariant functionals in Carnot groups. As a direct consequence, we can also provide a $\Gamma$-convergence result for a smaller class of functionals.
In this paper, we present a mixed-type integral-sum representation of the cylinder functions $\mathscr{C}_\mu(z)$, which holds for unrestricted complex values of the order $\mu$ and for any complex value of the variable $z$. Particular…
For free-probability Voiculescu transforms, analogous to hyperbolic characteristic functions, we show how to get their representing measures in an integral form. For that purpose, it is enough to know those transforms only on the imaginary…
This paper elaborates on a relationship between matrix-valued Herglotz-Nevanlinna functions and Hurwitz stable matrix polynomials, which generalizes the corresponding classical stability criterion. The main motivation comes from the…
We introduce and study multivariate zeta functions enumerating subrepresentations of integral quiver representations. For nilpotent such representations defined over number fields, we exhibit a homogeneity condition that we prove to be…
Generalization of the integral representation of the gamma function has been obtained, which shows that the Hankel contour assumes rotation in the complex plane. The range of admissible values for the contour rotation angle is set. Using…
In this paper, we find new integral representations for the generalized Hermite linear functional in the real line and the complex plane. As an application, new integral representations for the Euler Gamma function are given.
The main aim of this paper is to give a new generalization of Hurwitz-Lerch Zeta function of two variables.Also, we investigate several interesting properties such as integral representations, summation formula and a connection with…