Are the Fourier trigonometric basis orthogonal with respect to other weight besides the constant weight of one?

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Juan Weisz

Not that I have seen.

The proper framework for weight functions and very similar general structure to

Fourier is in Sturm-Liouville theory, which need not be limited to just one dimension. You just define orthogonality with respect to the weight function.

Or the example of the simple harmonic oscilator in quantum mechanics uses a weight function and Hermite functions, but you have to move into a special function world. It is a great field for exploration, that I am fond of.

Abdul Jerri

Greetings, Juan

I am thankful for your care to attempt answering my question.Yes, the variable weight,r(x) of the Sturm - Liouville problem, which, as a function of x, is associated with more genera1 orthogonal functions ,such as what you have mentioned, But not the the specific trigonometric( or complex exponential functions) of the usual Fourier series.

My question still Remains: Are the Fourier(Trigonometric) basis orthogonal with respect to a variable weight, besides the usual constant of one?

Many thanks

A.J.Jerri

[email protected],