Related papers: Sequence space representations for translation-mod…

This paper explores some important aspects of the theory of rearrangement-invariant quasi-Banach function spaces. We focus on two main topics. Firstly, we prove an analogue of the Luxemburg representation theorem for rearrangement-invariant…

In this paper, we give some properties of the modulation spaces $M_s^{p,1}({\mathbf R}^n)$ as commutative Banach algebras. In particular, we show the Wiener-L\'evy theorem for $M^{p,1}_s({\mathbf R}^n)$, and clarify the sets of spectral…

This paper is a survey of a new family of Banach spaces ${KS}^2$ and $SD^2$ that provide the same structure for the Henstock-Kurzweil (HK) integrable functions as the $L^p$ spaces provide for the Lebesgue integrable functions. These spaces…

It is shown that a covariant derivative on any d-dimensional manifold M can be mapped to a set of d operators acting on the space of functions on the principal Spin(d)-bundle over M. In other words, any d-dimensional manifold can be…

This paper is about the connection between certain Banach-algebraic properties of a commutative Banach algebra $E$ with unit and the associated commutative Banach algebra $C(X,E)$ of all continuous functions from a compact Hausdorff space…

The Lizorkin space is well-suited for studying various operators; e.g., fractional Laplacians and the Radon transform. In this paper, we show that the space is unfortunately not complemented in the Schwartz space. However, we can show that…

Given an infinite matrix $M=(m_{nk})$ we study a family of sequence spaces $\ell_M^p$ associated with it. When equipped with a suitable norm $\|\cdot\|_{M,p}$ we prove some basic properties of the Banach spaces of sequences…

We investigate integral representation of vector-valued function spaces, i.e., of subspaces $H\subset C(K,E)$, where $K$ is a compact space and $E$ is a (real or complex) Banach space. We point out that there are two possible ways of…

We adapt the classical theory of local well-posedness of evolution problems to cases in which the nonlinearity can be accurately quantified by two different norms. For ordinary differential equations, we consider $\dot{x} = f(x,x)$ for a…

Let A be a standard Borel space, and consider the space A^{\bbN^{(k)}} of A-valued arrays indexed by all size-k subsets of \bbN. This paper concerns random measures on such a space whose laws are invariant under the natural action of…

We present in this paper the Banach space representation for the set of random finite-dimensional vectors with exponential decreasing tails of distributions. We show that there are at last three types of these multidimensional Banach…

Under the weak assumption on a Banach space $E$ that $E\oplus E$ embeds isomorphically into $E$, we provide a characterisation of when a Banach space $X$ coarsely embeds into $E$ via a single numerical invariant.

We study the space spanned by the integer shifts of a bivariate Gaussian function and the problem of reconstructing any function in that space from samples scattered across the plane. We identify a large class of lattices, or more generally…

In this lecture, we present some results on Gaussian (or Rademacher) random series of trace class operators, mainly due jointly with F. Lust-Piquard. We will emphasize the probabilistic reformulation of these results, as well as the open…

We consider the action of a real linear algebraic group $G$ on a smooth, real affine algebraic variety $M\subset \R^n$, and study the corresponding left regular $G$-representation on the Banach space $C_0(M)$ of continuous, complex valued…

We study the Banach space $D([0,1]^m)$ of functions of several variables that are (in a certain sense) right-continuous with left limits, and extend several results previously known for the standard case $m=1$. We give, for example, a…

Let $\cal M$ be a semi-finite von Neumann algebra equipped with a distinguished faithful, normal, semi-finite trace $\tau$. We introduce the notion of equi-integrability in non-commutative spaces and show that if a rearrangement invariant…

We introduce loop spaces (in the sense of derived algebraic geometry) into the representation theory of reductive groups. In particular, we apply the theory developed in our previous paper arXiv:1002.3636 to flag varieties, and obtain new…

Let $\Bc$ denote the real-valued functions continuous on the extended real line and vanishing at $-\infty$. Let $\Br$ denote the functions that are left continuous, have a right limit at each point and vanish at $-\infty$. Define $\acn$ to…

This paper investigates advanced notions of lineability and spaceability within the frameworks of sequence spaces and operator ideals. We propose the notion of \emph{Standard Sequence Classes} to provide an environment that unifies numerous…