Timeline for Multiplying functions on the unit square as generalized matrices
Current License: CC BY-SA 3.0
13 events
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| Sep 7, 2011 at 8:24 | comment | added | Neil Strickland | @Pietro: what Google search terms did you have in mind? While you are right that this is elementary and classical, it is not so easy to find an account of it if you do not know the right name and your mathematical background is in a different area. | |
| Sep 7, 2011 at 7:18 | history | edited | user2035 |
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| Sep 4, 2011 at 19:20 | vote | accept | Bruno Joyal | ||
| Sep 4, 2011 at 19:20 | comment | added | Bruno Joyal | Thank you all! As guessed, I know nothing of functional analysis. I'm happy to have a new way of thinking about integral transforms. | |
| Sep 4, 2011 at 15:17 | comment | added | Todd Trimble | The general form of product considered here, as generalized matrix product, is of course very general indeed :-). It reappears in other guises as, e.g., relational composition, composition of spans, of profunctors, etc. Related constructions include convolution products, and multiplication in incidence algebras. I wonders whether the OP is interested not so much in "elementary functional analysis" as such, but rather in general contexts where such "matrix products" behave well, and what sorts of constructions are possible to generalize. If so, it might be good to try a different question. | |
| Sep 4, 2011 at 7:14 | comment | added | Pietro Majer | This is a piece of elementary classical functional analysis, as a simple Googol search would have immediately revealed. For an elementary and detailed discussion you may like to have a look to the nice booklet by Halmos and Sunder, Integral Operator on $L^2$ spaces. Voting to close. | |
| Sep 4, 2011 at 4:28 | answer | added | ARupinski | timeline score: 3 | |
| Sep 4, 2011 at 3:58 | comment | added | Spice the Bird | I would also wonder if a trace could be defined. Further is this related to Trace class operators? | |
| Sep 4, 2011 at 3:54 | comment | added | Spice the Bird | In this framework, integral transforms are the same as multiplying a column matrix (a function) by a matrix. | |
| Sep 4, 2011 at 2:27 | comment | added | Gerald Edgar | Study some functional analysis, perhaps? | |
| Sep 4, 2011 at 2:17 | answer | added | Ivan Yudin | timeline score: 5 | |
| Sep 4, 2011 at 1:33 | comment | added | Will Jagy | I like it. I think there will be an uncountable set of eigenvalues with multiplicity, so the simplest meaning of determinant is not going to work out. But you can define things such as $e^{- t A}$ for one of these, as you have an identity. | |
| Sep 3, 2011 at 23:25 | history | asked | Bruno Joyal | CC BY-SA 3.0 |