2011/02/24 by Maurice A. de Gosson, de Gosson, Maurice, Franz Luef +1
Mathematics · Medicine · #Advanced Algebra and Geometry #FOS: Mathematics #FOS: Physical sciences #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods #Mathematical Physics (math-ph) #Medical Imaging Techniques and Applications #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.1102.5132
openalex publication_date 2011/02/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
There has recently been evidence for replacing the usual Weyl quantization\nprocedure by the older and much less known Born-Jordan rule. In this paper we\ndiscuss this quantization procedure in detail and relate it to recent results\nof Boggiato, De Donno, and Oliaro on the Cohen class. We begin with a\ndiscussion of some properties of Shubin's \τ-pseudo-differential calculus,\nwhich allows us to show that the Born-Jordan quantization of a symbol a is\nthe average for \τ\∈ lbrack0,1] of the \τ-operators with symbol a.\nWe study the properties of the Born-Jordan operators, including their\nsymplectic covariance, and give their Weyl symbol.\n