Timeline for In what sense does the Hermite expansion of a bounded smooth function converge?
Current License: CC BY-SA 4.0
9 events
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| Oct 23, 2023 at 23:13 | comment | added | Isaac | Thank you. I understand now. Could you perhaps answer the following question as well? mathoverflow.net/questions/457008/… | |
| Oct 23, 2023 at 18:44 | comment | added | Iosif Pinelis | @Isaac : You cannot get the uniform convergence on the entire real line to a bounded nonzero function $f$ -- because the partial sums of the Hermite expansion of $f$ are nonzero polynomials and thus unbounded on the real line. If you have any additional questions, please ask them elsewhere. | |
| Oct 23, 2023 at 17:53 | comment | added | Isaac | And, if we have "global" Lipschitz continuity, then the convergence is uniform on while real line. Could you check my judgement once more? | |
| Oct 23, 2023 at 16:07 | vote | accept | Isaac | ||
| Oct 23, 2023 at 14:57 | comment | added | Iosif Pinelis | @Isaac : Yes, this is correct. I have added a paragraph on this. | |
| Oct 23, 2023 at 14:56 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| Oct 23, 2023 at 14:17 | comment | added | Isaac | So, in my case where $f$ is bounded and "smooth", the Hermite expansion of $f$ converges "uniformly" to $f$ on any compact interval. Is this right, I guess? | |
| Oct 23, 2023 at 14:08 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| Oct 23, 2023 at 14:01 | history | answered | Iosif Pinelis | CC BY-SA 4.0 |