Timeline for Do partitions of unity exist if we impose additional conditions on the derivatives?

8 events

when toggle format	what		by	license	comment
Sep 6, 2013 at 13:43	comment	added	fedja		@Ritwik Glad to hear it :-). The moral is: ask exactly what you need and let other people generalize or consider partial cases. Unless you can solve the problem yourself, you never know what the first step or the first reduction should be.
Sep 6, 2013 at 13:14	vote	accept	Ritwik
Sep 6, 2013 at 13:14	comment	added	Ritwik		In any case, this is a great answer. This is exactly what I was after.
Sep 6, 2013 at 13:13	comment	added	Ritwik		I am sorry, you were absolutely right; there is no mistake in what you said. I was making a simple error.
Sep 6, 2013 at 12:30	comment	added	fedja		@Ritwik Let's see: $\varphi_0^2+\varphi_1^2=\psi^2$, $(\varphi_0')^2+(\varphi_1'^2)=\psi'^2+\psi^2(\theta')^2$, so, yes, $\psi_j^2$ should be there (unless the condition is that the pure sum of squared derivatives with coefficients $n_j^2$ is prescribed instead, in which case it shouldn't).
Sep 6, 2013 at 12:20	comment	added	Ritwik		When you are defining $\theta^{\prime}$, did you intend to put the $\psi_j^2$ on the rhs? If the $\psi_j^2$ is not there, then every thing works out as you have said, unless I am making some calculation mistake.
Sep 6, 2013 at 1:55	history	edited	fedja	CC BY-SA 3.0	added 8 characters in body
Sep 6, 2013 at 1:46	history	answered	fedja	CC BY-SA 3.0