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Topic: analytic function problem
Replies: 76   Last Post: Oct 28, 1996 11:08 AM

 Messages: [ Previous | Next ]
 Hunter James D. STA x4202 Posts: 21 Registered: 12/12/04
Re: analytic function problem
Posted: Sep 30, 1996 2:17 PM

In article <324FEC1A.4533@math.okstate.edu>,
David Ullrich <ullrich@math.okstate.edu> wrote:
>Christopher wrote:
>>
>> Hello,
>> Please tell me how to prove simply that an analytic function is a function of
>> z only, no z_bar.

>
> Using z* for the conjugate of z:
>
> You need to state the conclusion more precisely before this can be
>proved. We all agree that f(z) = z^2 is analytic, but f(z) = g(z*) for a
>certain function g , so f _is_ "a function of z*".

Yes, of course this is right.

For any function of z, say, y = f(z) = f(conj(z*)).

So, how about the following way to say this.

If y = f(z) is an analytic function of z then y is necessarily
not an analytic function of z*, and
if y = g(z*) is an analytic function
of z*, then y is necessarily not a function of z.

In either case, I think you could use chain rule would show that dz*/dz exists,
which can be easily shown to be false.

If y is an analytic function of z then
dy/dz = f'(z)

and if y is an analytic function of z*

dy/dz* = f'(z)dz/dz*

Does this do it?

Jim

Date Subject Author
9/30/96 Christopher
9/30/96 David Ullrich
9/30/96 Hunter James D. STA x4202
10/1/96 David Ullrich
9/30/96 ilias kastanas 08-14-90
9/30/96 Dik T. Winter
10/1/96 David Kastrup
10/1/96 Hunter James D. STA x4202
9/30/96 Zdislav V. Kovarik
9/30/96 Anne DeCampo
10/2/96 Christopher
10/1/96 Tleko
10/2/96 David Kastrup
10/3/96 Dik T. Winter
10/3/96 Tleko
10/3/96 David Ullrich
10/3/96 Tleko
10/3/96 Dik T. Winter
10/3/96 Tleko
10/3/96 Zdislav V. Kovarik
10/5/96 Tleko
10/5/96 Dik T. Winter
10/6/96 Tleko
10/6/96 David Ullrich
10/7/96 ilias kastanas 08-14-90
10/7/96 Tleko
10/7/96 Andreas Leitgeb
10/7/96 Andreas Leitgeb
10/7/96 ilias kastanas 08-14-90
10/8/96 Tleko
10/8/96 Zdislav V. Kovarik
10/8/96 ilias kastanas 08-14-90
10/9/96 David Ullrich
10/8/96 Jim Hunter
10/8/96 Tleko
10/9/96 David Kastrup
10/9/96 Ilias Kastanas
10/11/96 Tleko
10/12/96 ilias kastanas 08-14-90
10/12/96 Dik T. Winter
10/11/96 Tleko
10/11/96 Tleko
10/11/96 Tleko
10/11/96 Tleko
10/11/96 Tleko
10/12/96 Tleko
10/12/96 Sue Franklin
10/13/96 Ilias Kastanas
10/13/96 Tleko
10/13/96 Tleko
10/13/96 ilias kastanas 08-14-90
10/14/96 Dik T. Winter
10/13/96 Tleko
10/13/96 Tleko
10/14/96 ilias kastanas 08-14-90
10/14/96 Dik T. Winter
10/15/96 Tleko
10/15/96 David Kastrup
10/15/96 Ilias Kastanas
10/16/96 Tleko
10/16/96 Dik T. Winter
10/17/96 Raymond DeCampo
10/18/96 Ariel Scolnicov
10/19/96 Tleko
10/19/96 Dik T. Winter
10/20/96 Terry Moore
10/21/96 Dik T. Winter
10/22/96 Ariel Scolnicov
10/20/96 Tleko
10/21/96 Terry Moore
10/22/96 David Kastrup
10/23/96 Tleko
10/24/96 Gunter Bengel
10/28/96 David Kastrup
10/28/96 David Ullrich