arXiv subjects
Publications and source records attributed to Emmanuel Fricain.
In this note, we describe the backward shift invariant subspaces for a large class of reproducing kernel Hilbert spaces. This class includes in particular de Branges-Rovnyak spaces (the non-extreme case) and the range space of co-analytic Toeplitz operators.
Recently, M. Mitkovski gave a criterion for the basicity of a sequence of complex exponentials in terms of the invertibility properties of a certain naturally associated Toeplitz operator, in the spirit of the celebrated work of Khrushchev-Nikolski-Pavlov. In our paper, we extend the results of Mitkovski to model spaces associated with meromorphic inner functions and we also give an analogue for the property of being an asymptotically orthonormal basis.
In this paper we discuss the multipliers between range spaces of co-analytic Toeplitz operators.
In this paper we examine the multipliers from one model space to another.
We emphasize a bridge between two areas of function theory: hilbertian Müntz spaces and model spaces of the Hardy space of the right half plane. We give miscellaneous applications of this viewpoint to hilbertian Müntz spaces.
In this note, we study the multipliers from one model space to another. In the case when the corresponding inner functions are meromorphic, we give both necessary and sufficient conditions ensuring this set of multipliers is not trivial. Our conditions involve the Beurling--Malliavin densities and are based on the deep work of Makarov--Poltoratski on injectivity of Toeplitz operators.
An asymptotically orthonormal sequence is a sequence which is 'nearly' orthonormal in the sense that it satisfies the Parseval equality up to two constants close to one. In this paper, we explore such sequences formed by normalized reproducing kernels of model spaces and de Branges Rovnyak spaces.
This is a survey on reverse Carleson measures for various Hilbert spaces of analytic functions. These spaces include Hardy, Bergman, certain harmonically weighted Dirichlet, Paley-Wiener, Fock, model, and de Branges-Rovnyak spaces.
Truncated Toeplitz operators are compressions of Toeplitz operators on model spaces; they have received much attention in the last years. This survey article presents several recent results, which relate boundedness, compactness, and spectra of these operators to properties of their symbols. We also connect these facts with properties of the natural embedding measures associated to these operators.
We discuss the range spaces of Toeplitz operators with co-analytic symbols where we focus on the boundary behavior of the functions in these spaces as well as a natural orthogonal decomposition of this range.
In this paper we give an explicit description of de Branges-Rovnyak spaces $\HH(b)$ when $b$ is of the form $q^{r}$, where $q$ is a rational outer function in the closed unit ball of $H^{\infty}$ and $r$ is a positive number.
We introduce a large family of reproducing kernel Hilbert spaces $\mathcal{H} \subset \mbox{Hol}(\mathbb{D})$, which include the classical Dirichlet-type spaces $\mathcal{D}_α$, by requiring normalized monomials to form a Riesz basis for $\mathcal{H}$. Then, after precisely evaluating the $n$-th optimal norm and the $n$-th approximant of $f(z)=1-z$, we completely characterize the cyclicity of functions in $\mbox{Hol}(\overline{\mathbb{D}})$ with respect to the forward shift.
In this paper we discuss direct and reverse Carleson measures for the de Branges-Rovnyak spaces $\mathcal{H}(b)$, mainly when b is a non-extreme point of the unit ball of $H^{\infty}$.
The classical embedding theorem of Carleson deals with finite positive Borel measures $μ$ on the closed unit disk for which there exists a positive constant $c$ such that $|f|_{L^2(μ)} \leq c |f|_{H^2}$ for all $f \in H^2$, the Hardy space of the unit disk. Lefévre et al. examined measures $μ$ for which there exists a positive constant $c$ such that $\|f\|_{L^2(μ)} \geq c |f|_{H^2}$ for all $f \in H^2$. The first type of inequality above was explored with $H^2$ replaced by one of the model spaces $(ΘH^2)^{\perp}$ by Aleksandrov, Baranov, Cohn, Treil, and Volberg. In this paper we discuss the second type of inequality in $(ΘH^2)^{\perp}$.
In this paper, using a generalization of a Richter and Sundberg representation theorem, we give a new characterization of Carleson measures for the Dirichlet-type space $\mathcal D(μ)$ when $μ$ is a finite sum of point masses. A reproducing kernel thesis result is also established in this case.
In this paper, we continue some work devoted to explicit zero-free discs for a large class of Dirichlet series. In a previous article, such zero-free regions were described using some spaces of functions which were defined with some technical conditions. Here we give two different natural ways in order to remove those technical conditions. In particular this allows to right down explicit zero-free regions differently and to obtain for them an easier description useful for direct applications.
We study the convergence of a sequence of finite Blaschke products of a fix order toward a rotation. This would enable us to get a better picture of a characterization theorem for finite Blaschke products.
In this paper, we are interested in explicit zero-free discs for some Dirichlet series and we also study a general Beurling-Nyman criterion for $L$-functions. Our results generalize and improve previous results obtained by N. Nikolski and by A. de Roton. As a concrete application, we get, for example, a Beurling-Nyman type criterion for the Siegel zero problem.