http://hdl.handle.net/10016/6199 Wed, 22 May 2013 12:07:36 GMT 2013-05-22T12:07:36Z http://hdl.handle.net/10016/8691 Title: On the tomographic picture of quantum mechanics Author(s): Ibort, Alberto; Man'ko, V. I.; Marmo, G.; Simoni, A.; Ventriglia, F. Abstract: We formulate necessary and sufficient conditions for a symplectic tomogram of a quantum state to determine the density state. We establish a connection between the (re)construction by means of symplectic tomograms with the construction by means of Naimark positive definite functions on the Weyl-Heisenberg group. This connection is used to formulate properties which guarantee that tomographic probabilities describe quantum states in the probability representation of quantum mechanics. Description: 4 pages, no figures.-- PACS codes: 03.65 Sq; 03.65.Wj.-- ArXiv pre-print available at: http://arxiv.org/abs/1004.0102 Sun, 06 Jun 2010 22:00:00 GMT http://hdl.handle.net/10016/8691 2010-06-06T22:00:00Z http://hdl.handle.net/10016/6316 Title: Oversampling in shift-invariant spaces with a rational sampling period Author(s): García, Antonio G.; Hernández-Medina, M. A.; Pérez-Villalón, G. Abstract: It is well known that, under appropriate hypotheses, a sampling formula allows us to recover any function in a principal shift-invariant space from its samples taken with sampling period one. Whenever the generator of the shift-invariant space satisfies the Strang-Fix conditions of order r, this formula also provides an approximation scheme of order r valid for smooth functions. In this paper we obtain sampling formulas sharing the same features by using a rational sampling period less than one. With the use of this oversampling technique, there is not one but an infinite number of sampling formulas. Whenever the generator has compact support, among these formulas it is possible to find one whose associated reconstruction functions have also compact support. Description: 8 pages, no figures. Mon, 31 Aug 2009 22:00:00 GMT http://hdl.handle.net/10016/6316 2009-08-31T22:00:00Z http://hdl.handle.net/10016/6310 Title: Alternative linear structures for classical and quantum systems Author(s): Ercolessi, E.; Ibort, Alberto; Marmo, G.; Morandi, G. Abstract: The possibility of deforming the (associative or Lie) product to obtain alternative descriptions for a given classical or quantum system has been considered in many papers. Here we discuss the possibility of obtaining some novel alternative descriptions by changing the linear structure instead. In particular we show how it is possible to construct alternative linear structures on the tangent bundle TQ of some classical configuration space Q that can be considered as "adapted" to the given dynamical system. This fact opens the possibility to use the Weyl scheme to quantize the system in different nonequivalent ways, "evading," so to speak, the von Neumann uniqueness theorem. Description: 26 pages, 2 figures.-- ArXiv pre-print available at: http://arxiv.org/abs/0706.1619 Thu, 31 May 2007 22:00:00 GMT http://hdl.handle.net/10016/6310 2007-05-31T22:00:00Z http://hdl.handle.net/10016/6307 Title: A brief walk through Sampling Theory Author(s): García, Antonio G. Abstract: Sampling Theory deals with the reconstruction of functions (signals) through their values (samples) on an appropriate sequence of points by means of sampling expansions involving these values. The most famous result in this direction is the Whittaker-Shannon-Kotel'nikov formula, which allows to reconstruct bandlimited signals (i.e., signals containing no frequencies beyond a critical value ωc) from an equidistant sequence of samples whose spacing depends on ωc. Description: 73 pages, 4 figures. Mon, 31 Dec 2001 23:00:00 GMT http://hdl.handle.net/10016/6307 2001-12-31T23:00:00Z