Related papers: A Beurling Theorem for Generalized Hardy Spaces on…

The classical Beurling-Helson-Lowdenslager theorem characterizes the shift-invariant subspaces of the Hardy space $H^{2}$ and of the Lebesgue space $L^{2}$. In this paper, which is self-contained, we define a very general class of norms…

A broader class of Hardy spaces and Lebesgue spaces have been introduced recently on the unit circle by considering continuous $\|.\|_1$-dominating normalized gauge norms instead of the classical norms on measurable functions and a Beurling…

In a recent paper, M. Raghupathi has extended the famous theorem of Beurling to the context of subspaces that are invariant under the class of subalgebras of $H^\infty$ of the form $IH^\infty$, where $I$ is an inner function. In this paper,…

We prove that the invariant subspaces of the Hardy operator on $L^2[0,1]$ are the spaces that are limits of sequences of finite dimensional spaces spanned by monomial functions.

How to extend Beurling's theorem on the shift invariant subspaces of Hardy class $H^2$ of the unit disk to several complex variables has been an open problem at least since 1964. In this paper, we prove a generalization of Beurling's…

We develop a theory of Valuation Hilbert Modules and prove a version of Beurling's theorem for these. Then we apply our version of Beurling's theorem to obtain complete descriptions of the closed invariant subspaces of a number of Hilbert…

The aim of this paper is to establish a canonical decomposition of operator-valued strong $L^2$-functions by the aid of the Beurling-Lax-Halmos Theorem which characterizes the shift-invariant subspaces of vector-valued Hardy space. This…

Let $G$ be a bounded open subset in the complex plane and let $H^{2}(G)$ denote the Hardy space on $G$. We call a bounded simply connected domain $W$ perfectly connected if the boundary value function of the inverse of the Riemann map from…

In this paper, we consider several questions emerging from the Beurling-Lax-Halmos Theorem, which characterizes the shift-invariant subspaces of vector-valued Hardy spaces. The Beurling-Lax-Halmos Theorem states that a backward…

In this paper we study some basic properties of bicomplex linear operators on bicomplex Hilbert spaces. Further we discuss some applications of Hahn-Banach theorem on bicomplex Banach modules. We also introduce and discuss some bicomplex…

A Helson-Lowdenslager type result has been proved by Chen in the context of Lebesgue spaces of the unit circle equipped with a continuous rotationally symmetric norm by studying the simply invariant subspaces of the operator of…

The invariant subspaces of the Hardy space on $H^2(\mathbb{D})$ of the unit disc are very well known however in several variables the structure of the invariant subspaces of the classical Hardy spaces is not yet fully understood. In this…

In a previous paper, we presented an Abstract Beurling's Theorem for valuation Hilbert modules over valuation algebras. In this paper, we shall apply this theorem to obtain complete descriptions of the closed invariant subspaces of a number…

In this paper we investigate the reproducing kernel Hilbert space where the polylogarithm appears as kernel functions. This investigation begins with the properties of functions in this space, and here a connection to the classical Hardy…

Using the notion of commutative operator vessels, this work investigates de Branges-Rovnyak spaces whose elements are sections of a line bundle of multiplicative half-order differentials on a compact real Riemann surface. As a special case,…

A complete characterization of nearly-invariant subspaces of finite defect for the backward shift operator acting on the Hardy space is provided in the spirit of Hitt and Sarason's theorem. As a corollary we describe the almost-invariant…

This paper focuses on representations of contractively embedded invariant subspaces in several variables. We present a version of the de Branges theorem for $n$-tuples of multiplication operators by the coordinate functions on analytic…

Yanni Chen extended the classical Beurling-Helson-Lowdenslager Theorem for Hardy spaces on the unit circle $\mathbb{T}$ defined in terms of continuous gauge norms on $L^{\infty}$ that dominate $\Vert\cdot\Vert_{1}$. We extend Chen's result…

We present some old and new results on a class of invariant spaces of holomorphic functions on symmetric domains, both in their circular bounded realizations and in their unbounded realizations as Siegel domains of type II. These spaces…

In this paper, we prove the boundedness of multilinear fractional integral operators from products of Hardy spaces associated with ball quasi-Banach function spaces into their corresponding ball quasi-Banach function spaces. As…