Timeline for What can we say about the left inverse of the Green's function?

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Apr 13, 2017 at 12:19	history	edited	CommunityBot		replaced http://math.stackexchange.com/ with https://math.stackexchange.com/
May 16, 2014 at 20:46	answer	added	Igor Khavkine		timeline score: 3
May 16, 2014 at 19:50	comment	added	Shiu		This question is motivated by my post on MathStackExchange (please follow the link above).
May 16, 2014 at 18:21	comment	added	k3thomps		Can I ask what you need the left inverse for? It isn't clear to me how it would be useful.
May 16, 2014 at 18:16	history	edited	Shiu	CC BY-SA 3.0	self-adjointness added
May 16, 2014 at 18:15	comment	added	Shiu		I need self-adjointness. Thank you for pointing out that. I am not sure what to do with the case where $f \not \in \mathrm{Dom}(\mathbb{D})$. This subtlety is part of my question and so I want to understand how to formulate the left inverse.
May 16, 2014 at 17:26	comment	added	k3thomps		You have to be careful. What if $f\notin Domain(\mathbb{D})$? What if $\mathbb{D}$ is not self adjoint (i.e. how do you know that the second integral you wrote down holds true if $\mathbb{D}$ is not self adjoint)? Also, as you pointed out the Fredholm alternative says that you can't solve $\mathbb{D} u = f$ if $f\in ker(\mathbb{D})$.
May 16, 2014 at 16:47	review	First posts
May 16, 2014 at 17:07
May 16, 2014 at 16:27	history	asked	Shiu	CC BY-SA 3.0