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Consider,

[tex] f(\mathbf{w}) = \int K(\mathbf{w,\mathbf{v}}) g(\mathbf{v}) d\mathbf{v} [/tex]

where [itex]\mathbf{v},\mathbf{w} \in \mathbb{R^3}[/itex].

Is it possible to solve for the integral kernel, [itex] K(\mathbf{w,\mathbf{v}}) [/itex], if [itex] f(\mathbf{w}) [/itex] and [itex] g(\mathbf{v}) [/itex], are known scalar functions and we require [itex] \int K(\mathbf{w,\mathbf{v}}) d\mathbf{v} = 1 [/itex]? These are definite integrals: [itex]\int \rightarrow \int_{a1}^{b1}\int_{a2}^{b2}\int_{a3}^{b3}[/itex]

Thank you for any solution/advice/insight!

[tex] f(\mathbf{w}) = \int K(\mathbf{w,\mathbf{v}}) g(\mathbf{v}) d\mathbf{v} [/tex]

where [itex]\mathbf{v},\mathbf{w} \in \mathbb{R^3}[/itex].

Is it possible to solve for the integral kernel, [itex] K(\mathbf{w,\mathbf{v}}) [/itex], if [itex] f(\mathbf{w}) [/itex] and [itex] g(\mathbf{v}) [/itex], are known scalar functions and we require [itex] \int K(\mathbf{w,\mathbf{v}}) d\mathbf{v} = 1 [/itex]? These are definite integrals: [itex]\int \rightarrow \int_{a1}^{b1}\int_{a2}^{b2}\int_{a3}^{b3}[/itex]

Thank you for any solution/advice/insight!

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