Related papers: A Variation on Selberg's Approximation Problem

Let $\Omega\subset\mathbb{C}^n$ be a product of one-dimensional open bounded domains with $C^{1,\alpha}$ boundary, where $0<\alpha<1$. Using methods from complex analysis in one variable, we construct an integral operator that solves…

For a sequence of uniformly bounded, degenerate semigroups on a Hilbert space, we compare various types of convergences to a limit semigroup. Among others, we show that convergence of the semigroups, or of the resolvents of the generators,…

We prove a Caffarelli--Kohn--Nirenberg inequality in the hyperbolic space. For a semilinear elliptic equation involving the associated weighted Laplace--Beltrami operator, we establish variationally the existence of positive radial…

Let $n\geq2$ and $ \Omega\subset \mathbb{R}^{n+1}$ be a Lipschitz wedge- like domain . We construct positive weak solutions of the problem $$\Delta u + u^p = 0 \quad\hbox{in}\, \Omega,$$ which vanish in a suitable trace sense on…

Let $S(\sigma,t)=\frac{1}{\pi}\arg\zeta(\sigma+it)$ be the argument of the Riemann zeta-function at the point $\sigma+it$ in the critical strip. For $n\geq 1$ and $t>0$, we define \begin{equation*} S_{n}(\sigma,t) = \int_0^t…

Capillarity functionals are parameter invariant functionals defined on classes of two-dimensional parametric surfaces in R3 as the sum of the area integral and a non homogeneous term of suitable form. Here we consider the case of a class of…

A priori estimates for semilinear higher order elliptic equations usually have to deal with the absence of a maximum principle. This note presents some regularity estimates for the polyharmonic Dirichlet problem that will make a distinction…

In this paper, we establish hybrid results on Diophantine approximation with primes from short intervals. In particular, we prove the following result in a slightly modified form: If $\alpha$ is an irrational number having a continued…

The paper is devoted to the investigation of Segal's entropy in semifinite von Neumann algebras. The following questions are dealt with: semicontinuity, the 'ideal-like' structure of the linear span of the set of operators with finite…

Let $\varphi:\mathbb{R}\rightarrow \mathbb{R}$ be a continuously differentiable function on an interval $J\subset\mathbb{R}$ and let $\boldsymbol{\alpha}=(\alpha_1,\alpha_2)$ be a point with algebraic conjugate integer coordinates of degree…

In this paper, applied strictly monotonic increasing scaled maps, a kind of well-conditioned linear barycentric rational interpolations are proposed to approximate functions of singularities at the origin, such as $x^\alpha$ for $\alpha \in…

We prove a determinantal formula for quantities related to the problem of enumeration of (semi-) meanders, namely the topologically inequivalent planar configurations of non-self-intersecting loops crossing a given (half-) line through a…

Let $f:[0,+\infty) \to \mathbb{R}$ be a (locally) Lipschitz function and $\Omega \subset \mathbb{R}^2$ a $C^{1,\alpha}$ domain whose boundary is unbounded and connected. If there exists a positive bounded solution to the overdetermined…

We construct majorants and minorants of a Gaussian function in Euclidean space that have Fourier transforms supported in a box. The majorants that we construct are shown to be extremal and our minorants are shown to be asymptotically…

This is the first installment in a series of papers devoted to examining certain aspects of the asymptotic value distribution and distribution of zeros manifested by members of a broad class of linear combinations of L-functions in the…

We introduce the notion of $\imath$Schur superalgebra, which can be regarded as a type B/C counterpart of the $q$-Schur superalgebra (of type A) formulated as centralizer algebras of certain signed $q$-permutation modules over Hecke…

Let $M$ be a maximal subalgebra of a Lie algebra $L$ and $A/B$ a chief factor of $L$ such that $B \subseteq M$ and $A \not \subseteq M$. We call the factor algebra $M \cap A/B$ a $c$-section of $M$. All such $c$-sections are isomorphic, and…

Let $S(C_0(X))^+$ and $S(C_0(Y))^+$ denote the positive parts of the unit spheres of $C_0(X)$ and $C_0(Y)$, where $X$ and $Y$ are locally compact Hausdorff spaces. We prove that every surjective isometry from $S(C_0(X))^+$ onto…

In this paper, we have proved Selberg's Central Limit Theorem for $GL(3)$ $L$-functions associated with the Hecke-Maass cusp form $f$. Moreover, we have proved the independence of the automorphic $L$-functions.

We show how a rescaling of fractional operators with bounded kernels may help circumvent their documented deficiencies, for example, the inconsistency at zero or the lack of inverse integral operator. On the other hand, we build a novel…