add BO equation #65
add BO equation #65
Conversation
- add Hilbert_{\R}{f}(z), the Hilbert transform on the real line for
periodic functions on [a,b). This is equivalent to the cotangent
version. However, it breaks with the convention of the package that the
domain of integration of the singular integral operator should be
defined by the domainspace. Perhaps this case could be an exception?
fix a typo in periodicline
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Probably PeriodicInterval should actually be the line, and evaluation defined for all R by moding. I can't think of an example where you actually want the current behaviour. We could even rename PeriodicIntercal to "Torus" (, periodicline is used already to mean a conformally mapped circle.) Sent from my iPhone
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The Benjamin-Ono equation with periodic boundary conditions (as implemented) has periodic analogues to solitons, so I think that would be interesting to some. http://www.diva-portal.org/smash/get/diva2:617038/FULLTEXT01.pdf I guess we just need to figure out what to call the real line with periodicity, i.e. f(t+b-a) = f(t) for all t in R. I don't think you need to mod for evaluation if the basis is periodic too, it's the perfect extrapolation. |
time evolution uses BDF2 basis is LaurentDirichlet(PeriodicLine())
# Conflicts: # test/runtests.jl
# Conflicts: # src/stieltjesmoment.jl
periodic functions on [a,b). This is equivalent to the cotangent
version. However, it breaks with the convention of the package that the
domain of integration of the singular integral operator should be
defined by the domainspace. Perhaps this case could be an exception?