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
asked Sep 6 at 9:05
KYHSGeekCode
187110
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up vote
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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
asked Sep 6 at 9:05
KYHSGeekCode
187110
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
add a comment |Â
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
asked Sep 6 at 9:05
KYHSGeekCode
187110
- 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
asked Sep 6 at 9:05
KYHSGeekCode
187110
asked Sep 6 at 9:05
KYHSGeekCode
187110
edited Sep 15 at 13:14
asked Sep 6 at 9:05
KYHSGeekCode
187110
asked Sep 6 at 9:05
KYHSGeekCode
187110
asked Sep 6 at 9:05
KYHSGeekCode
187110
187110
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
add a comment |Â
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
add a comment |Â
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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