In this paper is proven that all relations between a couple
of dual operators ) B,A( i.e. operators obeying the commutation relation I B,A are invariant under substitution of ) B,A( with any another
dual couple. From this property are obtained many differential operators
realizing transformations in space and phase space such as translation,
dilatation, hyperbolic, … , fractional order Fourier transforms and Fourier
transform itself. Transforms of arbitrary functions and operators and geometric
forms by these differential operators are given. The kernel of the integral
transform associated with a differential transform is found. As case study the
differential Fourier transform is highlighted in order to see how it is
possible to get in a concise manner the known properties of the Fourier
transform without doing integrations.
Author(s) Details
Author(s) Details
Do Tan Si
HoChiMinh-City Physical Association, 40 Dong Khoi, Q1, TP.HCM, Vietnam and Université libre de Bruxelles and UEM, Belgium.
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Book :- http://bp.bookpi.org/index.php/bpi/catalog/book/214HoChiMinh-City Physical Association, 40 Dong Khoi, Q1, TP.HCM, Vietnam and Université libre de Bruxelles and UEM, Belgium.
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