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Michael Hardy
Michael Hardy
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Let $L$ be an elliptic operator on $\Bbb C$ with $$\DeclareMathOperator{\Img}{Im} L^{-1}f(z)=\int_{\Bbb {C}}K_1(|z-w|^2)f(w) e^{i\cdot\Img\langle z,\overline{w}\rangle} dw $$$$\DeclareMathOperator{\Img}{Im} L^{-1}f(z)=\int_{\Bbb {C}}K_1(|z-w|^2)f(w) e^{i\cdot\Img\langle z,\overline{w}\rangle} \, dw $$ where $K_1$ is the modified Bessel function. I want to define the kernel Poisson to the Dirichlet problem $Lu=0 $ on the unit Ball $B$ of $\Bbb C$ with $u=f$ on the sphere $S$. How can I do that? Thank you in advance.

Let $L$ be an elliptic operator on $\Bbb C$ with $$\DeclareMathOperator{\Img}{Im} L^{-1}f(z)=\int_{\Bbb {C}}K_1(|z-w|^2)f(w) e^{i\cdot\Img\langle z,\overline{w}\rangle} dw $$ where $K_1$ is the modified Bessel function. I want to define the kernel Poisson to the Dirichlet problem $Lu=0 $ on the unit Ball $B$ of $\Bbb C$ with $u=f$ on the sphere $S$. How can I do that? Thank you in advance.

Let $L$ be an elliptic operator on $\Bbb C$ with $$\DeclareMathOperator{\Img}{Im} L^{-1}f(z)=\int_{\Bbb {C}}K_1(|z-w|^2)f(w) e^{i\cdot\Img\langle z,\overline{w}\rangle} \, dw $$ where $K_1$ is the modified Bessel function. I want to define the kernel Poisson to the Dirichlet problem $Lu=0 $ on the unit Ball $B$ of $\Bbb C$ with $u=f$ on the sphere $S$. How can I do that? Thank you in advance.

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Ryo Ken
Ryo Ken
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Let $L$ be an elliptic operator on $\Bbb C$ with $$\DeclareMathOperator{\Img}{Im} L^{-1}f(z)=\int_{\Bbb {C}}K_1(|z-w|^2)f(w) e^{i\cdot\Img\langle z,\overline{w}\rangle} dw $$ where $K_1$ is the modified Bessel function. I want to define the kernel Poisson to the Dirichlet problem $Lu=0 $ on the unit Ball $B$ of $\Bbb C$ with $u=f$ on the sphere $S$. How can I do that? Thank youinyou in advance.

Let $L$ be an elliptic operator on $\Bbb C$ with $$\DeclareMathOperator{\Img}{Im} L^{-1}f(z)=\int_{\Bbb {C}}K_1(|z-w|^2)f(w) e^{i\cdot\Img\langle z,\overline{w}\rangle} dw $$ where $K_1$ is the modified Bessel function. I want to define the kernel Poisson to the Dirichlet problem $Lu=0 $ on the unit Ball $B$ of $\Bbb C$ with $u=f$ on the sphere $S$. How can I do that? Thank youin advance.

Let $L$ be an elliptic operator on $\Bbb C$ with $$\DeclareMathOperator{\Img}{Im} L^{-1}f(z)=\int_{\Bbb {C}}K_1(|z-w|^2)f(w) e^{i\cdot\Img\langle z,\overline{w}\rangle} dw $$ where $K_1$ is the modified Bessel function. I want to define the kernel Poisson to the Dirichlet problem $Lu=0 $ on the unit Ball $B$ of $\Bbb C$ with $u=f$ on the sphere $S$. How can I do that? Thank you in advance.

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Daniele Tampieri
Daniele Tampieri
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Let $L$ be an elliptic operator on $\Bbb C$ with $L^{-1}f(z)=\int_{\Bbb {C}}K_1(|z-w|^2)f(w) e^{i.Im<z,\overline{w}>} dw$ with $$\DeclareMathOperator{\Img}{Im} L^{-1}f(z)=\int_{\Bbb {C}}K_1(|z-w|^2)f(w) e^{i\cdot\Img\langle z,\overline{w}\rangle} dw $$ where $K_1$ is the modified Bessel function. I want to define the kernel Poisson to the Dirichlet problem $Lu=O $$Lu=0 $ on the unit Ball $B$ of $\Bbb C$ with $u=f$ on the sphere $S$. How can I do that.? Thank youin advance.

Let $L$ be an elliptic operator on $\Bbb C$ with $L^{-1}f(z)=\int_{\Bbb {C}}K_1(|z-w|^2)f(w) e^{i.Im<z,\overline{w}>} dw$ with $K_1$ is the modified Bessel function. I want to define the kernel Poisson to the Dirichlet problem $Lu=O $ on the unit Ball $B$ of $\Bbb C$ with $u=f$ on the sphere $S$. How I do that. Thank youin advance.

Let $L$ be an elliptic operator on $\Bbb C$ with $$\DeclareMathOperator{\Img}{Im} L^{-1}f(z)=\int_{\Bbb {C}}K_1(|z-w|^2)f(w) e^{i\cdot\Img\langle z,\overline{w}\rangle} dw $$ where $K_1$ is the modified Bessel function. I want to define the kernel Poisson to the Dirichlet problem $Lu=0 $ on the unit Ball $B$ of $\Bbb C$ with $u=f$ on the sphere $S$. How can I do that? Thank youin advance.

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Ryo Ken
Ryo Ken
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