Related papers: Paley-Wiener isomorphism over infinite-dimensional…

The article is devoted to the problem of Hilbert-Schmidt type analytic extensions in Hardy spaces over the infinite-dimensional unitary matrix group endowed with an invariant probability measure. An orthogonal basis of Hilbert-Schmidt…

We outline an abstract approach to the pseudo-differential Weyl calculus for operators in function spaces in infinitely many variables. Our earlier approach to the Weyl calculus for Lie group representations is extended to the case of…

We extend the Paley--Wiener theorem for riemannian symmetric spaces to an important class of infinite dimensional symmetric spaces. For this we define a notion of propagation of symmetric spaces and examine the direct (injective) limit…

We investigate the group $\mathcal{H}_\mathbb{C}$ of complexified Heisenberg matrices with entries from an infinite-dimensional complex Hilbert space $H$. Irreducible representations of the Weyl--Schr{\"o}dinger type on the space $L^2_\chi$…

Polynomial invariants are fundamental objects in analysis on Lie groups and symmetric spaces. Invariant differential operators on symmetric spaces are described by Weyl group invariant polynomial. In this article we give a simple criterion…

In this paper we study spaces of holomorphic functions on the Siegel upper half-space $\mathcal U$ and prove Paley-Wiener type theorems for such spaces. The boundary of $\mathcal U$ can be identified with the Heisenberg group $\mathbb H_n$.…

Polynomial invariants are fundamental objects in analysis on Lie groups and symmetric spaces. Invariant differential operators on symmetric spaces are described by Weyl group invariant polynomial. In this article we give a simple criterion…

We investigate the Schr\"odinger representations of certain infinite-dimensional Heisenberg groups, using their corresponding Wigner transforms.

Infinite analogues of the Paley graphs are constructed, based on uncountably many infinite but locally finite fields. Weil's estimate for character sums shows that they are all isomorphic to the random or universal graph of Erd\H os,…

We survey some aspects of the pseudo-differential Weyl calculus for irreducible unitary representations of nilpotent Lie groups, ranging from the classical ideas to recently obtained results. The classical Weyl-H\"ormander calculus is…

We prove several Paley--Wiener-type theorems related to the spherical transform on the Gelfand pair $\big(H_n\rtimes U(n),U(n)\big)$, where $H_n$ is the $2n+1$-dimensional Heisenberg group. Adopting the standard realization of the Gelfand…

We represent closed subspaces of the Hardy space that are invariant under finite-rank perturbations of the backward shift. We apply this to classify almost invariant subspaces of the backward shift and represent a more refined version of…

We formulate and prove a version of Paley-Wiener theorem for the inverse Fourier transform on non-compact Riemannian symmetric spaces and Heisenberg groups. The main ingredient in the proof is the Gutzmer's formula.

We give a complete characterization of invariant subspaces for $(M_{z_1}, \ldots, M_{z_n})$ on the Hardy space $H^2(\mathbb{D}^n)$ over the unit polydisc $\mathbb{D}^n$ in $\mathbb{C}^n$, $n >1$. In particular, this yields a complete set of…

We discuss relations between uniform minimality, unconditionality and interpolation for families of reproducing kernels in backward shift invariant subspaces. This class of spaces contains as prominent examples the Paley-Wiener spaces for…

We characterize invariant subspaces of Brownian shifts on vector-valued Hardy spaces. We also solve the unitary equivalence problem for the invariant subspaces of these shifts.

A complexified Heisenberg matrix group $\mathrm{H}_\mathbb{C}$ with entries from an infinite-dimensional Hilbert space $H$ is investigated. The Weyl--Schr\"odinger type irreducible representations of $\mathrm{H}_\mathbb{C}$ on the space…

For certain nilpotent real Lie groups constructed as semidirect products, algebras of invariant differential operators on some coadjoint orbits are used in the study of boundedness properties of the Weyl-Pedersen calculus of their…

In this paper, the structure of the nearly invariant subspaces for discrete semigroups generated by several (even infinitely many) automorphisms of the unit disc is described. As part of this work, the near $S^*$-invariance property of the…

We prove a sampling theorem for infinite-dimensional Paley-Wiener spaces on graphs which allows for stable frame reconstruction. We prove that all sampling sets for a fixed Paley-Wiener space are complements of lambda-sets (i.e. sets where…