Ingrid Beltiţă

Uncertainty principles for magnetic structures on certain coadjoint orbits

Abstract By building on our earlier work, we establish uncertainty principles in terms of Heisenberg inequalities and of the ambiguity functions associated with magnetic structures on certain coadjoint orbits of infinite-dimensional Lie groups. These infinite-dimensional Lie groups are semidirect products of nilpotent Lie groups and invariant function spaces thereon. The recently developed magnetic Weyl calculus is recovered in the special case of function spaces on abelian Lie groups.

Local Smoothing for the Backscattering Transform

An analysis of the backscattering data for the Schrödinger operator in odd dimensions n ≥ 3 motivates the introduction of the backscattering transform . This is an entire analytic mapping and we write where B N v is the Nth order term in the power series expansion at v = 0. In this paper we study estimates for B N v in H (s) spaces, and prove that Bv is entire analytic in v ∈ H (s) ∩ ℰ′ when s ≥ (n − 3)/2.

INVERSE SCATTERING IN A LAYERED MEDIUM

We present a uniqueness theorem in inverse scattering at a fixed energy for the wave equation in a layered medium. We accommodate the Faddeev theory of inverse scattering using the calculus of commutators.

On Wigner transforms in infinite dimensions

We investigate the Schrodinger representations of certain infinite-dimensional Heisenberg groups, using their corresponding Wigner transforms.

Symbol calculus of square-integrable operator-valued maps

We develop an abstract framework for the investigation of quantization and dequantization procedures based on orthogonality relations that do not necessarily involve group representations. To illustrate the usefulness of our abstract method we show that it behaves well with respect to the infinite tensor products. This construction subsumes examples coming from the study of magnetic Weyl calculus, the magnetic pseudo-differential Weyl calculus, the metaplectic representation on locally compact abelian groups, irreducible representations associated with finite-dimensional coadjoint orbits of some special infinite-dimensional Lie groups, and the square-integrability properties shared by arbitrary irreducible representations of nilpotent Lie groups.

Representations of Nilpotent Lie Groups via Measurable Dynamical Systems

We study unitary representations associated to cocycles of measurable dynamical systems. Our main result establishes conditions on a cocycle, ensuring that ergodicity of the dynamical system under consideration is equivalent to irreducibility of its corresponding unitary representation. This general result is applied to some representations of finite-dimensional nilpotent Lie groups and to some representations of infinite-dimensional Heisenberg groups.

Boundedness for Pseudo-differential Calculus on Nilpotent Lie Groups

We survey a few results on the boundedness of operators arising from the Weyl–Pedersen calculus associated with irreducible representations of nilpotent Lie groups.

Inverse scattering in a layered medium

Abstract We present a uniqueness theorem in inverse scattering at a fixed energy for the wave equation in a layered medium. We accomodate the Faddeev theory of inverse scattering using the calculus of commutators.

Berezin Symbols on Lie Groups

In this paper we present a general framework for Berezin covariant symbols, and we discuss a few basic properties of the corresponding symbol map, with emphasis on its injectivity in connection with some problems in representation theory of nilpotent Lie groups.

Transference for Banach space representations of nilpotent Lie groups. Part 1. Irreducible representations

We study multipliers and