Timeline for Approximation of a two-variable function by tensor products
Current License: CC BY-SA 4.0
13 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 15, 2019 at 21:44 | answer | added | Dirk Werner | timeline score: 3 | |
| Jan 14, 2019 at 22:33 | comment | added | Dirk Werner | @Richard: Do you require Piotr's condition only for $x$ (that can be done) or also for $y$ (I don't see that...)? | |
| Jan 12, 2019 at 5:00 | comment | added | Richard | @Piotr Yes, that is enough as well. Thanks. | |
| Jan 11, 2019 at 20:02 | comment | added | Piotr Hajlasz | @Richard I think uniform bout of $k_n$ by a constant independent of $n$ is not possible. Also the second estimate seems not possible. However, $\sup_x\sup_n\sum_i|f_i^{(1,n)}(x)|<\infty$ is more likely to be true. Would it be enough? That is my rough guess. | |
| Jan 11, 2019 at 19:19 | comment | added | Richard | @Piotr ideally I would want $k_n$ to be uniformly bounded to get my desired rate of convergence in my proof. Alternatively, I can require $ \sup_{n \in \mathbb{N}} \sum_{i=1}^{k_n} \sup_{x \in X} \Big| f^{(1,n)}_i(x) \Big| < +\infty$ | |
| Jan 11, 2019 at 17:19 | comment | added | Piotr Hajlasz | @Richard Do you want $k_n\leq n$ or some other bound will suffice? | |
| Jan 11, 2019 at 7:41 | comment | added | Richard | @DirkWerner I just realised that, in my proof, I also need the sequence $k_n$ to be bounded in $n$. Do you think that partition of unity still works? Thanks. | |
| Jan 11, 2019 at 7:39 | history | edited | Richard | CC BY-SA 4.0 |
added 53 characters in body
|
| Jan 11, 2019 at 0:11 | comment | added | Richard | @Dirk Sorry can you give more details? One possible choice of partition of unity of $X \times Y$ consists of products of univariate functions of $X$ and $Y$. But after multiplying each function by $f$ ( not necessarily a product of univariate functions), the product itself is still not necessarily a product of univariate functions... | |
| Jan 10, 2019 at 21:04 | comment | added | Dirk Werner | Sorry - partitions of unity... | |
| Jan 10, 2019 at 19:41 | comment | added | Dirk Werner | Doesn't one use partions of unity multiplied by values of $f$ to get those univariate functions, and doesn't that show that the answer is yes? | |
| Jan 10, 2019 at 18:28 | history | edited | Richard | CC BY-SA 4.0 |
added 18 characters in body
|
| Jan 10, 2019 at 17:57 | history | asked | Richard | CC BY-SA 4.0 |