The object of the present work is to introduce a new “pseudodifferential” analysis on the real line. This alternative analysis is endowed with just as many symmetries as the usual one, mostly of a different nature. It is a necessary counterpart of the celebrated Weyl calculus, so far as certain matters pertaining to representation theory or modular form theory are concerned. Whether it may be of any use, in the foreseeable future, in partial differential equations, the most important domain of applications of pseudodifferential analysis, is much more questionable, though we shall try to give some minimal hints regarding related possibilities.
KeywordsModular Form Discrete Series Principal Series Symbolic Calculus Holomorphic Modular Form
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