Re: Coincidince of analytic functions

bryant_j_j@xxxxxxxxx writes:

Hi all,

Suppose f_1 and f_2 are complex functions analytic on the unit disc but
_not_ on the unit circle. Suppose also that f_1 and f_2 take on the
same values for a sequence z_1,z_2,... of points on the unit disc which
converges to a point of the unit circle. Does this imply that f_1=f_2,

Obviously not, since for instance f_1 could be identically 0, and f_2
could be 0 on the (open) unit disk and arbitrary on the unit circle.

or are other additional conditions required?

Continuity would certainly assure this, but presumably you want less
than that.

I think I saw results of
this type in Knopp's book on complex functions but can't recall it
exactly. Does anyone know about the results I am looking for? A hint of
the associated proof would also be appreciated.

One kind of answer would involve the phrase "Hardy space", I think.
What is the intended application? That might jog a memory here or
there.

Lee Rudolph
.

Relevant Pages

  • Re: Coincidince of analytic functions
    ... lrudolph@xxxxxxxxx (Lee Rudolph) wrote: ... Suppose f_1 and f_2 are complex functions analytic on the unit disc but ... along a sequence converging to a boundary point as above. ... this type in Knopp's book on complex functions but can't recall it ...
    (sci.math)
  • Re: Coincidince of analytic functions
    ... Suppose f_1 and f_2 are complex functions analytic on the unit disc but ... Continuity would certainly assure this, ... along a sequence converging to a boundary point as above. ... this type in Knopp's book on complex functions but can't recall it ...
    (sci.math)
  • Coincidince of analytic functions
    ... Suppose f_1 and f_2 are complex functions analytic on the unit disc but ... same values for a sequence z_1,z_2,... ... this type in Knopp's book on complex functions but can't recall it ... A hint of ...
    (sci.math)
  • Re: Coincidince of analytic functions
    ... Suppose f_1 and f_2 are complex functions analytic on the unit disc but ... same values for a sequence z_1,z_2,... ... converges to a point of the unit circle. ... in this context. ...
    (sci.math)
  • Re: Coincidince of analytic functions
    ... could be 0 on the unit disk and arbitrary on the unit circle. ... analytic on the unit disc, ... are those of the Statistics Department or of Purdue University. ... Herman Rubin, Department of Statistics, Purdue University ...
    (sci.math)
Quantcast