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Equivalent norms in some spaces of analytic functions and the uncertainty principle

Boris Paneah (1996)

Banach Center Publications

The main object of this work is to describe such weight functions w(t) that for all elements f L p , Ω the estimate w f p K ( Ω ) f p is valid with a constant K(Ω), which does not depend on f and it grows to infinity when the domain Ω shrinks, i.e. deforms into a lower dimensional convex set Ω . In one-dimensional case means that K ( σ ) : = K ( Ω σ ) as σ → 0. It should be noted that in the framework of the signal transmission problem such estimates describe a signal’s behavior under the influence of detection and amplification. This work...

Jordan- and Lie geometries

Wolfgang Bertram (2013)

Archivum Mathematicum

In these lecture notes we report on research aiming at understanding the relation beween algebras and geometries, by focusing on the classes of Jordan algebraic and of associative structures and comparing them with Lie structures. The geometric object sought for, called a generalized projective, resp. an associative geometry, can be seen as a combination of the structure of a symmetric space, resp. of a Lie group, with the one of a projective geometry. The text is designed for readers having basic...

Nonlinear Dirac equations.

Ng, Wei Khim, Parwani, Rajesh R. (2009)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

On the quantal nature of the Coulomb field

Andrzej Staruszkiewicz (1997)

Banach Center Publications

It is shown that the total electric charge, as determined from the Gauss law, is a quantum object. The argument is based on elementary considerations concerning the number of photons, which should be large in a classical situation.

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