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This article gives explicit integral formulas for the so-called generalized metaplectic operators, i.e. Fourier integral operators (FIOs) of Schr\"odinger type, having a symplectic matrix as canonical transformation. These integrals are…

We study the boundedness of Toeplitz-type operators defined in the context of the Calder\'on reproducing formula considering the specific wavelets whose Fourier transforms are related to Laguerre polynomials. Some sufficient conditions for…

We study mapping properties of Toeplitz operators $T_\mu$ associated to nonnegative Borel measure $\mu$ on the complex space $\mathbb{C}^n$. We, in particular, describe the bounded and compact operators $T_\mu$ acting between Fock spaces in…

We study a specific class of Fourier integral operators characterized by symbols belonging to the multi-parameter H\"ormander class $\mathbf{S}^m(\R^{ n_1} \times \R^{ n_2} \times \cdots \times \R^{n_d} )$, where $n= n_1 + n_2 +\cdots +…

Let $X$ be a separable Banach space endowed with a non-degenerate centered Gaussian measure $\mu$ and let $w$ be a positive function on $X$ such that $w\in W^{1,s}(X,\mu)$ and $\log w\in W^{1,t}(X,\mu)$ for some $s>1$ and $t>s'$. In the…

We study the weighted compactness and boundedness of Toeplitz operators on the Fock spaces. Fix $\alpha>0$. Let $T_{\varphi}$ be the Toeplitz operator on the Fock space $F^2_{\alpha}$ over $\mathbb{C}^n$ with symbol $\varphi\in L^{\infty}$.…

In this paper, we are interested in the construction of a bilinear pseudodifferential calculus. We define some symbolic classes which contains those of Coifman-Meyer. These new classes allow us to consider operators closely related to the…

We aim at constructing an analog of the Weyl calculus in an infinite dimensional setting, in which the usual configuration and phase spaces are ultimately replaced by infinite dimensional measure spaces, the so-called abstract Wiener…

We lay some mathematically rigorous foundations for the resolution of differential equations with respect to semi-classical bases and topologies, namely Freud-Sobolev polynomials and spaces. In this quest, we uncover an elegant theory…

We introduce the Hardy spaces $\mathcal{H}^{p}_{FIO}(\mathbb{R}^{n})$ for Fourier integral operators for $0<p<1$, thereby extending earlier constructions for $1\leq p\leq \infty$. We then establish various properties of these spaces,…

The paper is devoted to the study of Gamma white noise analysis. We define an extended Fock space $\Gama(\Ha)$ over $\Ha=L^2(\R^d, d\sigma)$, and show how to include the usual Fock space ${\cal F} (\Ha)$ in it as a subspace. We introduce in…

Let us denote ${\cal V}$, the finite dimensional vector spaces of functions of the form $\psi(x) = p_n(x) + f(x) p_m(x)$ where $p_n(x)$ and $p_m(x)$ are arbitrary polynomials of degree at most $n$ and $m$ in the variable $x$ while $f(x)$…

We consider a class of translationally invariant magnetic fields such that the corresponding potential has a constant direction. Our goal is to study basic spectral properties of the Schr\"odinger operator ${\bf H}$ with such a potential.…

An integral of the Wigner function of a wavefunction |psi >, over some region S in classical phase space is identified as a (quasi) probability measure (QPM) of S, and it can be expressed by the |psi > average of an operator referred to as…

Indicial operators are model operators associated to an elliptic differential operator near a corner singularity on a stratified manifold. These model operators are defined on generalized tangent cone configurations and exhibit a natural…

We obtain a general expression for a Wigner transform (Wigner function) on symmetric spaces of non-compact type and study the Weyl calculus of pseudodifferential operators on them.

In this paper we characterize hyperbolic cosine transforms of (positive) Borel measures $\nu$ in terms of exponential convexity (Bernstein's terminology). The case of compactly supported measures $\nu$ is also considered. All of this is…

We solve the following problems associated with Toeplitz operators $T_{\Phi}$ on Hilbert space-valued Hardy spaces $H_{\mathcal{E}}^2(\mathbb{D}^n)$ over the unit polydisc $\mathbb{D}^n$. $(I)$ Given operator-valued bounded analytic…

We construct phase space localizing operators in all dimensions. These are frequency localized variants of the conditional expectation operator related to a dyadic stopping time. Our construction is an improvement over the so-called phase…

By analytic perturbations, we refer to shifts that are finite rank perturbations of the form $M_z + F$, where $M_z$ is the unilateral shift and $F$ is a finite rank operator on the Hardy space over the open unit disc. Here shift refers to…