What are examples of ORTHOGONAL function space for multivariable functions?

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  • What are examples of orthogonal spaces of multivariable functions?

I asked a question and learned that $$langle f(x_1,x_2,cdots x_n),g(x_1,x_2,cdots x_n) rangle = idotsint_D f(x_1,x_2,cdots x_n) overlineg(x_1,x_2,cdots x_n) dx_1dx_2cdots dx_n$$.






multivariable-calculus functions orthogonality multivalued-functions







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  • 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 6 at 14:28










  • @random Does that requires multiple integrals?
    – KYHSGeekCode
    Sep 6 at 14:34










  • For a multidimensional variable space that is to be expected.
    – random
    Sep 6 at 14:53














up vote
0
down vote

favorite












  • What are examples of orthogonal spaces of multivariable functions?

I asked a question and learned that $$langle f(x_1,x_2,cdots x_n),g(x_1,x_2,cdots x_n) rangle = idotsint_D f(x_1,x_2,cdots x_n) overlineg(x_1,x_2,cdots x_n) dx_1dx_2cdots dx_n$$.






multivariable-calculus functions orthogonality multivalued-functions







share|cite|improve this question























  • 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 6 at 14:28










  • @random Does that requires multiple integrals?
    – KYHSGeekCode
    Sep 6 at 14:34










  • For a multidimensional variable space that is to be expected.
    – random
    Sep 6 at 14:53












up vote
0
down vote

favorite









up vote
0
down vote

favorite











  • What are examples of orthogonal spaces of multivariable functions?

I asked a question and learned that $$langle f(x_1,x_2,cdots x_n),g(x_1,x_2,cdots x_n) rangle = idotsint_D f(x_1,x_2,cdots x_n) overlineg(x_1,x_2,cdots x_n) dx_1dx_2cdots dx_n$$.






multivariable-calculus functions orthogonality multivalued-functions







share|cite|improve this question















  • What are examples of orthogonal spaces of multivariable functions?

I asked a question and learned that $$langle f(x_1,x_2,cdots x_n),g(x_1,x_2,cdots x_n) rangle = idotsint_D f(x_1,x_2,cdots x_n) overlineg(x_1,x_2,cdots x_n) dx_1dx_2cdots dx_n$$.






multivariable-calculus functions orthogonality multivalued-functions




multivariable-calculus functions orthogonality multivalued-functions






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




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edited Sep 15 at 13:14

























asked Sep 6 at 9:05









KYHSGeekCode

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  • 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 6 at 14:28










  • @random Does that requires multiple integrals?
    – KYHSGeekCode
    Sep 6 at 14:34










  • For a multidimensional variable space that is to be expected.
    – random
    Sep 6 at 14:53
















  • 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 6 at 14:28










  • @random Does that requires multiple integrals?
    – KYHSGeekCode
    Sep 6 at 14:34










  • For a multidimensional variable space that is to be expected.
    – random
    Sep 6 at 14:53















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 6 at 14:28




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 6 at 14:28












@random Does that requires multiple integrals?
– KYHSGeekCode
Sep 6 at 14:34




@random Does that requires multiple integrals?
– KYHSGeekCode
Sep 6 at 14:34












For a multidimensional variable space that is to be expected.
– random
Sep 6 at 14:53




For a multidimensional variable space that is to be expected.
– random
Sep 6 at 14:53















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