In most cases of practical interest, the orthonormal basis comes from an integral or differential operator, in which case the series converges in the distribution sense.
In the ten years since I co-founded a brand agency, I've often been asked, "Who or what is your greatest professional influence?" And while I'd love to say something intellectual or provocative like "Steve Jobs, David Ogilvyvy" or "my father," the truth is, much of the wisdom I refer to on a daily basis comes from the comedic films of the 1980s.
The fundamental method to construct a wavelet basis comes from the concept of multiresolution analysis (MRA [13]).
For anyone born female, being judged on a daily basis comes with the territory.
The P.D.C.'s dozen members, appointed to the job and serving on a volunteer basis, come from the executive staffs of the city's libraries and museums, or are independent artists.
Health insurance, when it did emerge on a mass basis, came from the business world, as exemplified by the Kaiser shipyard story.
And at the center of it all, connecting the entire work and providing access routes to its outer regions, was a song whose musical basis came from the lone bastion of hope on pop radio in those dark days, Daryl Hall and John Oates.
"We have, on an individual basis, come much further on race than the North has.
The only young people decision-makers now meet on a daily basis come from privileged backgrounds.
However, in these modern applications, the basis typically comes first, and the abelian algebra might not even be made explicit.
