Related papers: A Characterization of One-component Inner Function…

In this paper we discuss the spectral properties of one-term symmetric differential operators of even order with interior singularity, namely, we determine the deficiency numbers, describe its self-adjoint extensions and their spectrum. It…

This paper is concerned with various fine properties of the functional \[ \mathbb{D}(A) = \int_{\mathbb{T}^n}{\text{det}}^\frac{1}{n-1}(A(x))\,dx \] introduced in [33]. This functional is defined on $X_p$, which is the cone of matrix fields…

The series $\theta (q,x):=\sum _{j=0}^{\infty}q^{j(j+1)/2}x^j$ converges for $|q|<1$ and defines a {\em partial theta function}. For any fixed $q\in (0,1)$ it has infinitely many negative zeros. It is known that for $q$ taking one of the…

We study the circle restrictions of inner functions of the unit disc showing that the local invertibility of a restriction is independent of its singularity set and proving a local characterization of analytic conditional expectations. We…

A version of Gromov's cup product lemma in which one factor is the (1,0)-part of the differential of a continuous plurisubharmonic function is obtained. As an application, it is shown that a connected noncompact complete Kaehler manifold…

We developed the theory of finite volume form factors in the presence of integrable defects. These finite volume form factors are expressed in terms of the infinite volume form factors and the finite volume density of states and incorporate…

Properties of four quintic theta functions are developed in parallel with those of the classical Jacobi null theta functions. The quintic theta functions are shown to satisfy analogues of Jacobi's quartic theta function identity and…

It is shown that a set in product of $n$ metrizable spaces is the discontinuity points set of some separately continuous function if and only if this set can be represented as the union of a sequence of $F_{\sigma}$-sets which are locally…

In courses on integration theory, Chasles property is usually considered as elementary and so "natural" that this is sometimes left to the reader. When the functions take their values in finite dimensional spaces, the property is always…

In this paper, we define a soft somewhat open set using the soft interior operator. We study main properties the class of soft somewhat open sets that is contained in the class soft somewhere dense sets. Then, we introduce the classes of…

We present a new approach to the static finite temperature correlation functions of the Heisenberg chain based on functional equations. An inhomogeneous generalization of the n-site density operator is considered. The lattice path integral…

We prove that a singular part $\mu_s$ of a measure $\mu$ satisfying ${\cal A}\mu =0$ for a linear partial differential operator ${\cal A}$ defined on $R^d$ has the range in the intersection of kernels of the principal symbol of ${\cal A}$…

A well-known problem in holomorphic dynamics is to obtain Denjoy--Wolff-type results for compositions of self-maps of the unit disc. Here, we tackle the particular case of inner functions: if $f_n:\mathbb{D}\to\mathbb{D}$ are inner…

A classical result due to Blaschke states that for every analytic self-map $f$ of the open unit disk of the complex plane there exists a Blaschke product $B$ such that the zero sets of $f$ and $B$ agree. In this paper we show that there is…

We characterize real functions $f$ on an interval $(-\alpha,\alpha)$ for which the entrywise matrix function $[a_{ij}] \mapsto [f(a_{ij})]$ is positive, monotone and convex, respectively, in the positive semidefiniteness order. Fractional…

We consider the variation of two fundamental types of zeta functions that arise in the study of both physical and analytical problems in geometric settings involving conical singularities. These are the Barnes zeta functions and the Bessel…

Conventionally, one calculates a zero in a beta function by computing this function to a given loop order and solving for the zero. Here we discuss a different method which is applicable in theories where one can perform a partial…

In this paper we give a simple proof of inequalities of integrals of functions which are the composition of nonnegative continous convex functions on a vector space ${\bf R}^m$ and vector-valued functions in a weakly compact subset of a…

This theorem is based on holomorphy of studied functions and the fact that near a singularity point the real part of some rational function can take an arbitrary preassigned value.

The paper presents an integral representation of the two-parameter Mittag-Leffler function $E_{\rho,\mu}(z)$ and singular points of this representation have been studied. It has been found that there are two singular points for this…