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August 26th, 2012, 03:19 AM   #1
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If f(z) is analytic in the domain 0<Re(z)<1, then show that

If f(z) is analytic in the domain 0<Re(z)<1, then show that
1) f(1-z) is also analytic in the domain 0<Re(z)<1
2) f(z*) is analytic in the domain 0<Re(z)<1
Here z* is the conjugate of z.
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August 26th, 2012, 03:26 AM   #2
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Re: If f(z) is analytic in the domain 0<Re(z)<1, then show t

Can one tel me about this problem: Let us consider the series (sum an/n*s) if the coffecient an is depend on s, then it is true to consider this serie as a Dirichlet serie or not.
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August 26th, 2012, 05:49 AM   #3
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Re: If f(z) is analytic in the domain 0<Re(z)<1, then show t

Quote:
Originally Posted by zeraoulia
If f(z) is analytic in the domain 0<Re(z)<1, then show that
1) f(1-z) is also analytic in the domain 0<Re(z)<1
2) f(z*) is analytic in the domain 0<Re(z)<1
Here z* is the conjugate of z.
if then

This implies that f(1-z) and f(z*) are also analytic in D.

Balarka

.
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August 26th, 2012, 08:09 AM   #4
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Re: If f(z) is analytic in the domain 0<Re(z)<1, then show t

Thank you very much for your kind reply
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