Related papers: Translation-modulation invariant Banach spaces of …
In this article we show how certain irreducible unitary representation $ \Pi_\lambda $ of the twisted Heisenberg group $ \He_\lambda^n(\C)$ leads to the twisted modulation spaces $ M_\lambda^{p,q}(\R^{2n}).$ These $ \Pi_\lambda $ also turn…
The paper is devoted to Mellin convolution operators with meromorphic kernels in Bessel potential spaces. We encounter such operators while investigating boundary value problems for elliptic equations in planar 2D domains with angular…
In this paper we introduce the notion of weak differential subordination for martingales and show that a Banach space $X$ is a UMD Banach space if and only if for all $p\in (1,\infty)$ and all purely discontinuous $X$-valued martingales $M$…
We obtain some results for and further examples of subprojective and superprojective Banach spaces. We also give several conditions providing examples of non-reflexive superprojective spaces; one of these conditions is stable under…
Differentials on Riemann surfaces correspond to translation surfaces with conical singularities, and affine transformations acting on them preserve the orders of these singularities. This viewpoint allows the moduli spaces of differentials…
In this note, we introduce the notion of modulus of $p$-variation for a function of a real variable, and show that it serves in at least two important problems, namely, the uniform convergence of Fourier series and computation of certain…
The motivation that the field of differential equations provide to several researchers for the challenges that have been challenging them over the decades has contributed to the strengthening of the area within mathematics. In this sense,…
In this paper, we study stability properties of nonuniform hyperbolicity for evolution processes associated with differential equations in Banach spaces. We prove a robustness result of nonuniform hyperbolicity for linear evolution…
We study some questions concerning the structure of the set of spreading models of a separable infinite-dimensional Banach space $X$. In particular we give an example of a reflexive $X$ so that all spreading models of $X$ contain $\ell_1$…
A moduli space of stable quotients of the rank n trivial sheaf on stable curves is introduced. Over nonsingular curves, the moduli space is Grothendieck's Quot scheme. Over nodal curves, a relative construction is made to keep the torsion…
In this paper, a sufficient condition for the existence of hyperinvariant subspace of compact perturbations of multiplication operators on some Banach spaces is presented. An interpretation of this result for compact perturbations of normal…
We derive rates of convergence for the mixing of operators under infinitely divisible measures in the framework of linear dynamics on Banach spaces. Our approach is based on the characterization of mixing in terms of codifference…
Despite their ubiquity in core AI fields like natural language processing, the mechanics of deep attention-based neural networks like the Transformer model are not fully understood. In this article, we present a new perspective towards…
We study finite-rank left-translation invariant algebraic $D$-modules on complex affine algebraic groups. Using the standard description of these objects as left-invariant flat algebraic connections on the trivial vector bundle, modulo…
We study representations of Banach algebras on reflexive Banach spaces. Algebras which admit such representations which are bounded below seem to be a good generalisation of Arens regular Banach algebras; this class includes dual Banach…
The use of anisotropic Banach spaces has provided a wealth of new results in the study of hyperbolic dynamical systems in recent years, yet their application to specific systems is often technical and difficult to access. The purpose of…
In this paper, we will study the topological centers of $n-th$ dual of Banach $A-module$ and we extend some propositions from Lau and $\ddot{U}lger$ into $n-th$ dual of Banach $A-modules$. Let $B$ be a Banach $A-bimodule$. By using some new…
In this paper, we study the coarse embedding into Banach space. We proved that under certain conditions, the property of embedding into Banach space can be preserved under taking the union the metric spaces. For a group $G$ strongly…
This paper is devoted to give several characterizations on a more general level for the boundedness of $\tau$-Wigner distributions acting from weighted modulation spaces to weighted modulation and Wiener amalgam spaces. As applications,…
Interpretations of the Beurling-Lax-Halmos Theorem on invariant subspaces of the unilateral shift are explored using the language of Hilbert modules. Extensions and consequences are considered in both the one and multivariate cases with an…