On Generalized Functions in Adelic Quantum Mechanics
Abstract
Some aspects of adelic generalized functions, as linear continuous functionals on the space of SchwartzBruhat functions, are considered. The importance of adelic generalized functions in adelic quantum mechanics is demonstrated. In particular, adelic product formula for Gauss integrals is derived, and the connection between the functional relation for the Riemann zeta function and quantum states of the harmonic oscillator is stated.
 Publication:

arXiv eprints
 Pub Date:
 April 2004
 arXiv:
 arXiv:mathph/0404076
 Bibcode:
 2004math.ph...4076D
 Keywords:

 Mathematical Physics;
 11R56;
 46F99;
 81Q99
 EPrint:
 9pages