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I am wondering if the field of "Complex Analysis in One Variable" is different from the field called "Complex Function Theory". I hope this is not a ridiculous question, because I have tried finding out the difference on Wikipedia first, but "Complex Function Theory" had nothing come up.

Or is Complex Function Theory a subset of Operator Theory or is it different from it as well?

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    @Theo: heh, as $y$ou may have noticed be now my mathematical German is the level of "uninformed people". Thanks for informing me. `:-)`2011-06-29

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For the question as stated exactly, I would say that "complex analysis in one variable" is a subset of "complex function theory", which in principle can allow more than one variables. (If the question were about "complex analysis" without the qualifier "in one variable", I would completely agree with Pete and Tim's comments that they are two names for the same thing.)

In the AMS MSC, one complex variable is in 30-XX, while several complex variables is in 32-XX, reflecting the fact that there are important differences between the two sub-disciplines. So one may arguably say that the name "complex analysis" or "complex function theory" encompass two fields under the same heading.