Timeline for What's the name of this semi-group theorem?
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16 events
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| Aug 28, 2022 at 21:21 | comment | added | Tom Copeland | See my comments on Charles Graves in my MO-Q "In 'splendid isolation'" in my answer on quantum mechanics and my comments on Scherk in my other answer on rooted trees and numerical methods for differential equations. See also my comments in MO-Q "Origins of the generalized shift operator exp(t*g(z)d/dz)" concerning Scherk, Abel, and Charles Graves. | |
| Aug 28, 2022 at 16:32 | comment | added | askquestions2 | @TomCopeland Hi Tom, in your original post which you deleted, you mentioned someone else discovered the shift theorem before others, although also mentioned Abel discovered it before them too in the 1850s. Do you remember who you were talking about? | |
| Aug 27, 2022 at 19:15 | answer | added | Jochen Glueck | timeline score: 7 | |
| Aug 26, 2022 at 20:22 | comment | added | LSpice | @JochenGlueck, that is a good point. I was thinking, as you suggest, of the Banach algebra generated by $L$, but I think that there can be no argument that my comment was definitely appropriate (if at all) only as a comment, and not as an answer. (And certainly I did not mean to propose it as the best—although perhaps the most efficient—way to prove the result!) | |
| Aug 26, 2022 at 20:21 | comment | added | Jochen Glueck | @LSpice: When interpreting this as chain rule I believe one should add (which I did not in my previous comment - that is why I deleted the comment) that it is not completely trivial to determine the derivative of the exponential map on an operator space (or, more generally, on a non-commutative Banach algebra). To keep life easy, one could restrict to the Banach algebra generated by $L$, but in particular if one is mainly interested in the finite-dimensional case (OP mentioned ODEs), this is probably still overkill, and it's clearer, I think, to just prove the formula directly. | |
| Aug 26, 2022 at 20:04 | comment | added | LSpice | @TomCopeland, that is certainly true, and is why my comment was a comment, not an answer; but, re, I'm not sure that I'm ready to sign on to a point of view according to which operators are not functions, and even functions whose differentiability one can sensibly discuss. (Come to that, it is not $L$ that we are differentiating, but that's a trivial quibble.) | |
| Aug 26, 2022 at 16:23 | comment | added | askquestions2 | I think that's conflated with the chain rule for standard calculus of a single variable. This is surely more abstract than that case and it's used to prove the solution to linear systems of ordinary differential equations. | |
| Aug 26, 2022 at 16:10 | comment | added | LSpice | The chain rule? | |
| Aug 26, 2022 at 16:10 | history | edited | LSpice | CC BY-SA 4.0 |
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| Aug 26, 2022 at 16:08 | review | Close votes | |||
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| Aug 26, 2022 at 15:58 | history | edited | YCor |
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| Aug 26, 2022 at 15:48 | history | edited | askquestions2 | CC BY-SA 4.0 |
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| Aug 26, 2022 at 15:47 | history | edited | askquestions2 |
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| Aug 26, 2022 at 15:47 | history | edited | askquestions2 | CC BY-SA 4.0 |
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| S Aug 26, 2022 at 15:47 | review | First questions | |||
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| S Aug 26, 2022 at 15:47 | history | asked | askquestions2 | CC BY-SA 4.0 |