Timeline for Can curves induced by analytic maps wiggle infinitely across a line?
Current License: CC BY-SA 2.5
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| Apr 22, 2010 at 16:09 | comment | added | Thomas Scanlon | No, my functions are real valued. The function L has the form L(z) = a Re(z) + b Im(z) + c for some real numbers a, b and c. I am using the fact that if F(z) is complex analytic, then via the usual identification of C with R^2, the induced function G:R^2 -> R^2 given by (a,b) -> (Re(F(a+ib)),Im(F(a+ib))) is real analytic, a result one can see by expanding the Taylor series for F(a+ib). | |
| Apr 22, 2010 at 12:09 | comment | added | gowers | My comment does not imply that the question isn't straightforward. I am struggling to understand your argument, however. Are your "real analytic" functions complex-valued? I should add that the fact that I am struggling to understand your argument is compatible with its being clear and correct. | |
| Apr 22, 2010 at 7:26 | history | answered | Thomas Scanlon | CC BY-SA 2.5 |