Related papers: Examples of de Branges-Rovnyak spaces generated by…

Associated with every separable Hilbert space $\mathcal{H}$ and a given localized frame, there exists a natural test function Banach space $\mathcal{H}^1$ and a Banach distribution space $\mathcal{H}^{\infty}$ so that $\mathcal{H}^1 \subset…

We construct examples of finitely presented simple groups whose Dehn functions are at least exponential. To the best of our knowledge, these are the first such examples known. Our examples arise from R\"over-Nekrashevych groups, using…

Let $L$ be a non-negative self-adjoint operator on $L^2(\mathbb{R}^n)$ whose heat kernels have the Gaussian upper bound estimates. Assume that the growth function $\varphi:\,\mathbb{R}^n\times[0,\infty) \to[0,\infty)$ satisfies that…

Let $\mathcal{A}$ denote the class of analytic functions $f$ on the unit disk $\mathbb{D}=\{z\in\mathbb{C} : |z|<1\}$, normalized by $f(0)=0$ and $f^{\prime}(0)=1$. For $-\pi/2<\alpha<\pi/2$, let $\mathcal{S}_{\alpha}$ be the subclass of…

We introduce novel black hole (BH) solutions, charge/non-charge, within the framework of $f(R)$ gravity, a theory that does not inherently include a cosmological constant, using equal/diffirent metric ansatzs. Remarkably, these solutions…

The paper describes homomorphisms between Douglas algebras and some semisimple Banach algebras. The main tool is a result on the structure of the space $C(Z,\mathfrak M)$ of continuous mappings from a connected first-countable $T_1$ space…

We characterize the extreme and exposed points of the unit ball (with respect to the $L^1$-norm) in the shift-invariant space generated by the Gaussian function, as well as in the quasi shift-invariant space generated by the hyperbolic…

This paper studies the local spacings of deformations of the Riemann zeta function under certain averaging and differencing operations. For real h it considers A_h(s)= 1/2(xi(s+h)+ xi(s-h)) and B_h(s)=1/(2i)(xi(s+h)-xi(s-h)), where xi(s) is…

We study the problem of characterizing the cyclic vectors in de Branges-Rovnyak spaces. Based on a description of the invariant subspaces we show that the difficulty lies entirely in understanding the subspace $(aH^{2})^{\perp}$ and give a…

Let $H^\infty(\mathbb D\times\N)$ be the Banach algebra of bounded holomorphic functions defined on the disjoint union of countably many copies of the open unit disk $\mathbb D\subset\mathbb C$. We show that the dense stable rank of…

We study the dg-algebra $\Omega ^\bullet_{A|\mathbb{R}}$ of algebraic de Rham forms of a real soft function algebra $A$, i.e., the algebra of global sections of a soft subsheaf of $C_X$, the sheaf of continuous functions on a space $X$. We…

Let $\Delta_m$ be the standard $m$-dimensional simplex of non-negative $m+1$ tuples that sum to unity and let $S$ be a nonempty subset of $\Delta_m$. A real valued function $h$ defined on a convex subset of a real vector space is $S$-almost…

We prove that all extreme points of the unit ball of a Lipschitz-free space over a compact metric space have finite support. Combined with previous results, this completely characterizes extreme points and implies that all of them are also…

Let $p\in(1,\infty)$ and $q\in[1,\infty)$. In this article, the authors characterize the Triebel-Lizorkin space ${F}^\alpha_{p,q}(\mathbb{R}^n)$ with smoothness order $\alpha\in(0,2)$ via the Lusin-area function and the…

Let $\theta$ be an inner function on the unit disk, and let $K^p_\theta:=H^p\cap\theta\overline{H^p_0}$ be the associated star-invariant subspace of the Hardy space $H^p$, with $p\ge1$. While a nontrivial function $f\in K^p_\theta$ is never…

A new characterization of the exponential type Orlicz spaces generated by the functions $\exp(|x|^p)-1$ ($p\ge 1$) is given. We define norms for centered random variables belonging to these spaces. We show equivalence of these norms with…

Given a unital algebra $\mathscr A$ of locally Lipschitz functions defined over a metric measure space $({\mathrm X},{\mathsf d},\mathfrak m)$, we study two associated notions of function of bounded variation and their relations: the space…

We study representations of inner functions on the bidisc from a fractional linear transformation point of view, and provide sufficient conditions, in terms of colligation matrices, for the existence of two-variable inner functions. Here…

In this article, methods from sub-Hardy Hilbert spaces such as the de Branges-Rovnyak spaces and local Dirichlet spaces are used to investigate B\'aez-Duarte's Hilbert space reformulation of the Riemann hypothesis (RH).

For every Banach space $(Y,\|\cdot\|_Y)$ that admits an equivalent uniformly convex norm we prove that there exists $c=c(Y)\in (0,\infty)$ with the following property. Suppose that $n\in \mathbb{N}$ and that $X$ is an $n$-dimensional normed…