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  • What are examples of orthogonal spaces of multivariable functions?

I asked a question and learned that $$\langle f(x_1,x_2,\cdots x_n),g(x_1,x_2,\cdots x_n) \rangle = \idotsint_D f(x_1,x_2,\cdots x_n) \overline{g(x_1,x_2,\cdots x_n)} dx_1dx_2\cdots dx_n$$.

KYHSGeekCode
  • 777
  • For real-valued functions on a given domain a dot product can be defined as the integral over that domain of the product of those functions and a fixed non-negative weight function. The spherical harmonics are an example. – random Sep 06 '18 at 14:28
  • @random Does that requires multiple integrals? – KYHSGeekCode Sep 06 '18 at 14:34
  • For a multidimensional variable space that is to be expected. – random Sep 06 '18 at 14:53

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