Search results for "Group representation"

Representations of Finite Groups

2009

Isometric dilations and 𝐻^{∞} calculus for bounded analytic semigroups and Ritt operators

2017

We show that any bounded analytic semigroup on L p L^p (with 1 > p > ∞ 1>p>\infty ) whose negative generator admits a bounded H ∞ ( Σ θ ) H^{\infty }(\Sigma _\theta ) functional calculus for some θ ∈ ( 0 , π 2 ) \theta \in (0,\frac {\pi }{2}) can be dilated into a bounded analytic semigroup ( R t ) t ⩾ 0 (R_t)_{t\geqslant 0} on a bigger L p L^p -space in such a way that R t R_t is a positive contraction for any t ⩾ 0 t\geqslant 0 . We also establish a discrete analogue for Ritt operators and consider the case when L p L^p -spaces are replaced by more general Banach spaces. In connection with these functional calculus issues, we study isometric dilations of bounded continuous rep…

On large orbits of supersoluble subgroups of linear groups

2019

The research of this paper has been supported by the grant MTM2014-54707-C3-1-P from the Ministerio de Economia y Competitividad, Spain, and FEDER, European Union, by the grant PGC2018-095140-B-I00 from the Ministerio de Ciencia, Innovacion y Universidades and the Agencia Estatal de Investigacion, Spain, and FEDER, European Union, and by the grant PROMETEO/2017/057 from the Generalitat, Valencian Community, Spain. The first author is supported by the predoctoral grant 201606890006 from the China Scholarship Council. The second author is supported by the grant 11401597 from the National Science Foundation of Chin

Coherent states: a contemporary panorama

2012

Coherent states (CS) of the harmonic oscillator (also called canonical CS) were introduced in 1926 by Schr?dinger in answer to a remark by Lorentz on the classical interpretation of the wave function. They were rediscovered in the early 1960s, first (somewhat implicitly) by Klauder in the context of a novel representation of quantum states, then by Glauber and Sudarshan for the description of coherence in lasers. Since then, CS have grown into an extremely rich domain that pervades almost every corner of physics and have also led to the development of several flourishing topics in mathematics. Along the way, a number of review articles have appeared in the literature, devoted to CS, notably…

Some remarks on Landau's (macroscopic) phase transition theory

2012

This paper explain the existence of a particular formal model (drew from Theoretical Astrophysics) whose thermodynamical phenomenology shows a possible second order phase transition (according to Landau’s Thermodynamical Theory) that seems does not verify the (Birman-Goldrich-Jaric) ”chain subduction criterion” and the (Ascher’s) ”maximality criterion” of Landau’s Phenomenological Theory. Therefore, it follows that Landau’s Phenomenological Theory is more restrictive than the Landau’s Thermodynamical Theory.