Related papers: Monomial basis in Korenblum type spaces of analyti…

In the present note we give two explicit constructions (based on a retractional argument) of a Schauder basis for the Lipschitz free space $\mathcal{F}(N)$, over certain uniformly discrete metric spaces $N$. The first one applies to every…

We study the class $\mathcal C$ of symmetric functions whose coefficients in the Schur basis can be described by generating functions for sets of tableaux with fixed shape. Included in this class are the Hall-Littlewood polynomials,…

Let ${\mathcal A}$ be the class of functions analytic in the unit disk ${\mathbb D} := \{ z\in {\mathbb C}:\, |z| < 1 \}$ and normalized such that $f(z)=z+a_2z^2+a_3z^3+\cdots$. In this paper we study the class $\mathcal{U}(\lambda)$,…

Using methods of descriptive set theory, in particular, the determinacy of infinite games of perfect information, we answer several questions from the literature regarding different notions of bases in Banach spaces and lattices. For the…

Let $\gamma\in\mathbb{R}\setminus\{0\}$ and $X(\mathbb{R}^n)$ be a ball Banach function space satisfying some extra mild assumptions. Assume that $\Omega=\mathbb{R}^n$ or $\Omega\subset\mathbb{R}^n$ is an $(\varepsilon,\infty)$-domain for…

Let ${\mathcal U}(\lambda)$ denote the family of analytic functions $f(z)$, $f(0)=0=f'(0)-1$, in the unit disk $\ID$, which satisfy the condition $\big |\big (z/f(z)\big )^{2}f'(z)-1\big |<\lambda $ for some $0<\lambda \leq 1$. The…

We give a sufficient and necessary condition for an analytic function $f(z)$ on the unit ball $\BB$ in $\CC^n$ with Hadamard gaps, that is, for $f(z)=\sum_{k=1}^\infty P_{n_k}(z)$ where $P_{n_k}(z)$ is a homogeneous polynomial of degree…

We introduce and study a generalization $s_{(\mu|\lambda)}$ of the Schur functions called the almost symmetric Schur functions. These functions simultaneously generalize the finite variable key polynomials and the infinite variable Schur…

We show that if $X$ is a Banach space with a Schauder basis, $\Omega\subset X$ is a pseudoconvex open subset, and $u:\,\Omega\to(-\infty,\infty)$ is a locally bounded function, then there are a Banach space $Z$ and a holomorphic function…

A Banach space with a Schauder basis is said to be $\alpha$-minimal for some countable ordinal $\alpha$ if, for any two block subspaces, the Bourgain embeddability index of one into the other is at least $\alpha$. We prove a dichotomy that…

We consider the space $\bk^1_{\log^\alpha}$, of analytic functions on the unit disk $\D,$ defined by the requirement $\int_\D|f'(z)|\phi(|z|)\,dA(z)<\infty,$ where $\phi(r)=\log^\alpha(1/(1-r))$ and show that it is a predual of the…

We introduce a non-commutative Walsh system and prove that it forms a Schauder basis in the Lp-spaces (1 < p < \infty) associated with the hyperfinite III_\lambda-factors (0 < \lambda <= 1).

We provide a characterization of the Banach spaces $X$ with a Schauder basis $(e_n)_{n\in\mathbb{N}}$ which have the property that the dual space $X^*$ is naturally isomorphic to the space $\mathcal{L}_{diag}(X)$ of diagonal operators with…

Let $f_{\bf c}(r)=\sum_{n=0}^\infty e^{c_n}r^n$ be an analytic function; ${\bf c}=(c_n)\in l_\infty$. We assume that $r$ is some logarithmically convex and lower semicontinuous functional on a locally convex topological space $L$. In this…

We investigate asymptotic polynomial approximation for a class of weighted Bloch functions in the unit disc. Our main result is a structural theorem on asymptotic polynomial approximation in the unit disc, in the flavor of the classical…

Let $A$ be a monomial associative finite dimensional algebra over a field $\Bbbk$ of characteristic zero. It is well known that the Hochschild cohomology of $A$ can be computed using Bardzell's complex $B(A)$. The aim of this article is to…

We introduce the Banach spaces $\ell^p_{a,b}$ and $c_{0,a,b}$, of analytic functions on the unit disc, having normalized Schauder bases consisting of polynomials of the form $f_n(z)=(a_n+b_nz)z^n, ~~n\geq0$, where $\{f_n\}$ is assumed to be…

Let ${\mathbb{D}}=\{z\in \mathbb{C}:|z|<1\}$ and for an integer $d\geq 1$, let $S_d$ denote the symmetric group, consisting of of all permutations of the set $\{1,\cdots, d\}$. A function $f:{\mathbb{D}}^d\rightarrow \mathbb{C}$ is…

We study the space, $R_m$, of $m$-symmetric functions consisting of polynomials that are symmetric in the variables $x_{m+1},x_{m+2},x_{m+3},\dots$ but have no special symmetry in the variables $x_1,\dots,x_m$. We obtain $m$-symmetric…

We give a generalization of the notion of finite Blaschke products from the perspective of generalized inner functions in various reproducing kernel Hilbert spaces. Further, we study precisely how these functions relate to the so-called…