In order to acquire with simplicity the characteristics of linear recognized transformations (LCTs), it is introduced the idea of dual couple of operators bearing commutator identical to unity and the feature that all relations betwixt them are valuable for any different dual couple. It follows that from the translation controller exp (a∂x) which transforms the two-fold couple (∂x, x^ ) into (∂x, x^ + al) one obtains the extension operator exp (aBA) which transfers the dual couple (A, B) into (e -al A, e -al B) then the driver exp (aA2) exp (aB2) and so all, leading to the building of general uninterrupted and linear canonical revolutions in phase spaces. Moreover, are still obtained the LCT revamps of functions. By this way different types of LCTs such as Fast Fourier, Fourier, Laplace, Xin Ma and Rhodes, Baker-Campbell-Haussdorf, Bargman transforms are raise again. We also acquire a clear relationship middle from two points linear and linear accepted transforms from the formula acting as an agent the aforementioned integral realisation. Numerous LCT models are provided to climax the method's ease of use.
Author(s) Details:
Tan Si Do,
Ho Chi Minh-City Physical Association, Ho Chi
Minh City, Vietnam and Universite libre de Bruxelles, UEM, Bruxelles, Belgium.
Please see the link here: https://stm.bookpi.org/RHMCS-V8/article/view/10190
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