Insights Blog
-- Browse All Articles --
Physics Articles
Physics Tutorials
Physics Guides
Physics FAQ
Math Articles
Math Tutorials
Math Guides
Math FAQ
Education Articles
Education Guides
Bio/Chem Articles
Technology Guides
Computer Science Tutorials
Forums
Intro Physics Homework Help
Advanced Physics Homework Help
Precalculus Homework Help
Calculus Homework Help
Bio/Chem Homework Help
Engineering Homework Help
Trending
Featured Threads
Log in
Register
What's new
Search
Search
Search titles only
By:
Intro Physics Homework Help
Advanced Physics Homework Help
Precalculus Homework Help
Calculus Homework Help
Bio/Chem Homework Help
Engineering Homework Help
Menu
Log in
Register
Navigation
More options
Contact us
Close Menu
JavaScript is disabled. For a better experience, please enable JavaScript in your browser before proceeding.
You are using an out of date browser. It may not display this or other websites correctly.
You should upgrade or use an
alternative browser
.
Forums
Homework Help
Calculus and Beyond Homework Help
Show operator is compact/symmetric
Reply to thread
Message
[QUOTE="mathwonk, post: 6153194, member: 13785"] finitely many eigen[I]values[/I] is cool, but doesn't a compact symmetric operator on L2 have an infinite number of eigen[I]functions[/I]? Oh yes, the kernel seems to be the key. Note that for any smooth function F with F(0) = F(1) = integral of F over [0,1], the derivative F' seems to be in the kernel. These are very easy to construct with F(0) = 0. e.g. F(x) = sin(2nπx). but i have not checked this. Indeed the general theory seems to say that there are only finitely many eigenfunctions sharing the same ≠0 eigenvalue, but there can be infinitely many with eigenvalue zero. But this is not my game. It seems kind of fun though, and I used to like it back in the day. [/QUOTE]
Insert quotes…
Post reply
Forums
Homework Help
Calculus and Beyond Homework Help
Show operator is compact/symmetric
Back
Top