Related papers: On the continuous dual of the sequence space $bv$

We give analytic description for the completion of $C_0^\infty ( \mathbf{R}_+)$ in Dirichlet space $D^{1,p}(\mathbf{R}_+, \omega):= \{ u:\mathbf{R}_+\rightarrow \mathbf{R}: u\ \hbox{ is locally absolutely continuous on} \ \mathbf{R}_+ \…

In the setting of a metric space equipped with a doubling measure supporting a Poincar\'e inequality, we show that BV functions are, in the sense of multiple limits, continuous with respect to a 1-fine topology, at almost every point with…

We demonstrate the equivalence of two classes of $D$-invariant polynomial subspaces introduced in [8] and [9], i.e., these two classes of subspaces are different representations of the breadth-one $D$-invariant subspace. Moreover, we solve…

We apply the ideas of Muhly, Skeide and Solel [MSS03] of considering von Neumann B-modules as intertwiner spaces for representations of B' to obtain a new, simple and self-contained proof for self-duality of von Neumann modules. This…

In the setting of a metric space equipped with a doubling measure that supports a Poincar\'e inequality, we show that any set of finite perimeter can be approximated in the BV norm by a set whose topological and measure theoretic boundaries…

We parameterize by a fine moduli space all degenerations of linear series to a singular curve which is the union of two smooth components meeting transversally at a single point. For this we introduce a novel object in the study of…

We study relations between the variational Sobolev 1-capacity and versions of variational BV-capacity in a complete metric space equipped with a doubling measure and supporting a weak $(1,1)$-Poincar\'e inequality. We prove the equality of…

In the setting of a metric space $X$ equipped with a doubling measure that supports a Poincar\'e inequality, we show that if $u_i\to u$ strictly in $BV(X)$, i.e. if $u_i\to u$ in $L^1(X)$ and $\Vert Du_i\Vert(X)\to\Vert Du\Vert(X)$, then…

Given an open set \Omega\subset\R^m and n>1, we introduce the new spaces GB_nV(\Omega) of Generalized functions of bounded higher variation and GSB_nV(\Omega) of Generalized special functions of bounded higher variation that generalize,…

The classical Dirichlet space is a complete Pick space, hence by a theorem of Agler and McCarthy, there exists an embedding $b$ of the unit disc into a $d$-dimensional ball such that composition with $b$ realizes the Dirichlet space as a…

The main purpose of this note is to establish the continuity of seminorms on finite-dimensional vector spaces over the real or complex numbers.

SBV is a deep inference system that extends the set of logical operators of multiplicative linear logic with the non commutative operator Seq. We introduce the logical system SBVr which extends SBV by adding a self-dual atom-renaming…

By an extension of Harnad's and Dubrovin's `duality' constructions, the general isomonodromy problem studied by Jimbo, Miwa, and Ueno is equivalent to one in which the linear system of differential equations has a regular singularity at the…

The space $\mathscr B_{mt}[(m_j)_j,(n_j)_j]$ is a Bourgain-Delbaen space modelled on a mixed Tsirelson space $T[(m_j)_j,(n_j)_j]$ and is a slight modification of $\mathfrak B_{\text{mt}}[(m_j)_j,(n_j)_j]$, a space defined by S. Argyros and…

For $\sigma\in (0,+\infty)$, denote by $B_\sigma^{\infty}$ the Bernstein space (of type $\sigma$) of all entire functions of exponential type $\leq \sigma$ bounded on real axis $\R$. Let $I_d\subset \R$ be a segment of length $d>0$. We…

In a complete metric space that is equipped with a doubling measure and supports a Poincar\'e inequality, we show that functions of bounded variation (BV functions) can be approximated in the strict sense and pointwise uniformly by special…

We give three characterizations of the Dirichlet-type spaces $D(\mu)$. First we characterize $D(\mu)$ in terms of a double integral and in terms of the mean oscillation in the Bergman metric, none of them involve the use of derivatives.…

Objective of this paper is to introduce the generalized geometric difference sequence spaces $l_\infty^{G}(\Delta^m_G), c^G(\Delta^m_G), c_0^{G}(\Delta^m_G)$ and to prove that these are Banach spaces. Then we prove some inclusion…

The carriers of the still (mostly) unidentified diffuse interstellar bands (DIBs) have been a long-standing mystery ever since their first discovery exactly 100 years ago. In recent years, the ubiquitous detection of a large number of DIBs…

For $1\leq p\leq \infty$ and $\alpha>0$, Besov spaces $B^p_\alpha$ play a key role in the theory of $\alpha$-M\"obius invariant function spaces. In some sense, $B^1_\alpha$ is the minimal $\alpha$-M\"obius invariant function space,…