Real analytic potential 2
$begingroup$
Let $G(x,zeta)=|x-zeta|^{2-n}$, for $ngeq3$, and $$p(x)=int_{B(a,R
)}G(x,zeta)Delta u(zeta)dzeta$$
with $Delta$ meaning the laplacian, and $B(a,R
)$ the ball of center $a$ and radius $R>0$. Suppose $u$ is real analytic (and subharmonic). We know by Riesz decomposition theorem that in this case $p(x)$ is also real analytic. My question is: Can we have an estimate of the radius of convergence of the Taylor series of $p$ at $a$?
real-analysis potential-theory
asked Nov 27 '18 at 2:53
M. RahmatM. Rahmat
286212
$endgroup$
add a comment |
$begingroup$
Let $G(x,zeta)=|x-zeta|^{2-n}$, for $ngeq3$, and $$p(x)=int_{B(a,R
)}G(x,zeta)Delta u(zeta)dzeta$$
with $Delta$ meaning the laplacian, and $B(a,R
)$ the ball of center $a$ and radius $R>0$. Suppose $u$ is real analytic (and subharmonic). We know by Riesz decomposition theorem that in this case $p(x)$ is also real analytic. My question is: Can we have an estimate of the radius of convergence of the Taylor series of $p$ at $a$?
real-analysis potential-theory
asked Nov 27 '18 at 2:53
M. RahmatM. Rahmat
286212
$endgroup$
add a comment |
$begingroup$
Let $G(x,zeta)=|x-zeta|^{2-n}$, for $ngeq3$, and $$p(x)=int_{B(a,R
)}G(x,zeta)Delta u(zeta)dzeta$$
with $Delta$ meaning the laplacian, and $B(a,R
)$ the ball of center $a$ and radius $R>0$. Suppose $u$ is real analytic (and subharmonic). We know by Riesz decomposition theorem that in this case $p(x)$ is also real analytic. My question is: Can we have an estimate of the radius of convergence of the Taylor series of $p$ at $a$?
real-analysis potential-theory
asked Nov 27 '18 at 2:53
M. RahmatM. Rahmat
286212
$endgroup$
Let $G(x,zeta)=|x-zeta|^{2-n}$, for $ngeq3$, and $$p(x)=int_{B(a,R
)}G(x,zeta)Delta u(zeta)dzeta$$
with $Delta$ meaning the laplacian, and $B(a,R
)$ the ball of center $a$ and radius $R>0$. Suppose $u$ is real analytic (and subharmonic). We know by Riesz decomposition theorem that in this case $p(x)$ is also real analytic. My question is: Can we have an estimate of the radius of convergence of the Taylor series of $p$ at $a$?
real-analysis potential-theory
real-analysis potential-theory
asked Nov 27 '18 at 2:53
M. RahmatM. Rahmat
286212
asked Nov 27 '18 at 2:53
M. RahmatM. Rahmat
286212
asked Nov 27 '18 at 2:53
M. RahmatM. Rahmat
286212
asked Nov 27 '18 at 2:53
M. RahmatM. Rahmat
286212
asked Nov 27 '18 at 2:53
M. RahmatM. Rahmat
286212
286212
add a comment |
add a comment |
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