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YCor
YCor
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I have a function $A(x) = \int_{\partial B_1(0)} e^{ikx} B(k) dk$ in $3D$ and I want to find $B(k)$ for a given $A(x)$. How can I do that?

In my use case it would be enough to invert $R_n^m(x) = \int_{\partial B_1(0)} e^{ikx} S_n^m(k) dk$ with $R \in SO(3; \mathbb R) \forall x$$R \in \mathrm{SO}(3; \mathbb R)$, $\forall x$. Any help for the special or general case would be appreciated.

I have a function $A(x) = \int_{\partial B_1(0)} e^{ikx} B(k) dk$ in $3D$ and I want to find $B(k)$ for a given $A(x)$. How can I do that?

In my use case it would be enough to invert $R_n^m(x) = \int_{\partial B_1(0)} e^{ikx} S_n^m(k) dk$ with $R \in SO(3; \mathbb R) \forall x$. Any help for the special or general case would be appreciated.

I have a function $A(x) = \int_{\partial B_1(0)} e^{ikx} B(k) dk$ in $3D$ and I want to find $B(k)$ for a given $A(x)$. How can I do that?

In my use case it would be enough to invert $R_n^m(x) = \int_{\partial B_1(0)} e^{ikx} S_n^m(k) dk$ with $R \in \mathrm{SO}(3; \mathbb R)$, $\forall x$. Any help for the special or general case would be appreciated.

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Nextdorf
Nextdorf
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I have a function $A_n(x) = \int_{\partial B_1(0)} e^{ikx} B_n(k) dk$$A(x) = \int_{\partial B_1(0)} e^{ikx} B(k) dk$ in $3D$ and I want to find $B(k)$ for a given $A(x)$. How can I do that?

In my use case it would be enough to invert $R_n^m(x) = \int_{\partial B_1(0)} e^{ikx} S_n^m(k) dk$ with $R \in SO(3; \mathbb R) \forall x$. Any help for the special or general case would be appreciated.

I have a function $A_n(x) = \int_{\partial B_1(0)} e^{ikx} B_n(k) dk$ in $3D$ and I want to find $B(k)$ for a given $A(x)$. How can I do that?

In my use case it would be enough to invert $R_n^m(x) = \int_{\partial B_1(0)} e^{ikx} S_n^m(k) dk$ with $R \in SO(3; \mathbb R) \forall x$. Any help for the special or general case would be appreciated.

I have a function $A(x) = \int_{\partial B_1(0)} e^{ikx} B(k) dk$ in $3D$ and I want to find $B(k)$ for a given $A(x)$. How can I do that?

In my use case it would be enough to invert $R_n^m(x) = \int_{\partial B_1(0)} e^{ikx} S_n^m(k) dk$ with $R \in SO(3; \mathbb R) \forall x$. Any help for the special or general case would be appreciated.

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Nextdorf
Nextdorf
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Inversion of a Fourier-like transformation on $\partial B_1(0)$

I have a function $A_n(x) = \int_{\partial B_1(0)} e^{ikx} B_n(k) dk$ in $3D$ and I want to find $B(k)$ for a given $A(x)$. How can I do that?

In my use case it would be enough to invert $R_n^m(x) = \int_{\partial B_1(0)} e^{ikx} S_n^m(k) dk$ with $R \in SO(3; \mathbb R) \forall x$. Any help for the special or general case would be appreciated.