Timeline for Are there functions satisfying the following integral condition?
Current License: CC BY-SA 2.5
5 events
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| Jan 30, 2011 at 6:13 | comment | added | Chulumba | That's an interesting observation. However, one requirement is that $ f\neq g$ . So, the exponential map, even with the lower limit of integration replaced by minus infinity, fails one criterion. | |
| Jan 29, 2011 at 21:22 | comment | added | Lloyd Smith | Oh, ok! Well, the exponential map is also invariant under integration, and is also a solution here if you replace your lower limit of integration with minus infinity. | |
| Jan 29, 2011 at 14:34 | comment | added | Chulumba | (...continued) So, the natural curiosity to find a nontrivial map invariant under integration. For obvious reasons, such map does not exist because of the presence of the constant of integration in indefinite integrals. Hence, I added an extra condition that would make the would-be function more nontrivial and more appealing. | |
| Jan 29, 2011 at 14:26 | comment | added | Chulumba | Thanks for your comments. First, the quotation is not mine. It was the recently-late Arnold's way of joking when he told others about his conjectures. Second, the equation that I wrote out was not random. At least, the symmetry I find in it and the absence of an iota of clue at proceeding with any method makes me fall in love with finding a solution. Part of the motivation was to find a function that in some way resembles the exponential function. The exponential map is invariant under differentiation. (...continued..) | |
| Jan 29, 2011 at 9:14 | history | answered | Lloyd Smith | CC BY-SA 2.5 |