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Confining quantum particles with a purely magnetic field

Yves Colin de Verdière, Françoise Truc (2010)

Annales de l’institut Fourier

We consider a Schrödinger operator with a magnetic field (and no electric field) on a domain in the Euclidean space with a compact boundary. We give sufficient conditions on the behaviour of the magnetic field near the boundary which guarantees essential self-adjointness of this operator. From the physical point of view, it means that the quantum particle is confined in the domain by the magnetic field. We construct examples in the case where the boundary is smooth as well as for polytopes; These...

Conical Fourier-Borel transformations for harmonic functionals on the Lie ball

Mitsuo Morimoto, Keiko Fujita (1996)

Banach Center Publications

Let L(z) be the Lie norm on ˜ = n + 1 and L*(z) the dual Lie norm. We denote by Δ ( B ˜ ( R ) ) the space of complex harmonic functions on the open Lie ball B ˜ ( R ) and by E x p Δ ( ˜ ; ( A , L * ) ) the space of entire harmonic functions of exponential type (A,L*). A continuous linear functional on these spaces will be called a harmonic functional or an entire harmonic functional. We shall study the conical Fourier-Borel transformations on the spaces of harmonic functionals or entire harmonic functionals.

Conical measures and properties of a vector measure determined by its range

L. Rodríguez-Piazza, M. Romero-Moreno (1997)

Studia Mathematica

We characterize some properties of a vector measure in terms of its associated Kluvánek conical measure. These characterizations are used to prove that the range of a vector measure determines these properties. So we give new proofs of the fact that the range determines the total variation, the σ-finiteness of the variation and the Bochner derivability, and we show that it also determines the (p,q)-summing and p-nuclear norm of the integration operator. Finally, we show that Pettis derivability...

Connes amenability-like properties

Amin Mahmoodi (2014)

Studia Mathematica

We introduce and study the notions of w*-approximate Connes amenability and pseudo-Connes amenability for dual Banach algebras. We prove that the dual Banach sequence algebra ℓ¹ is not w*-approximately Connes amenable. We show that in general the concepts of pseudo-Connes amenability and Connes amenability are distinct. Moreover the relations between these new notions are also discussed.

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