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Oct
9 |
awarded | Nice Question |
Jul
29 |
awarded | Popular Question |
Feb
1 |
comment |
Fourier Coefficients and Hölder Continuity
Thank you for the great diagram and explanation. Is there a reason that this problem becomes easy again for $C^{\infty}$ functions? |
Feb
1 |
comment |
Fourier Coefficients and Hölder Continuity
Thanks! Is there a text or paper where I can find this result? |
Feb
1 |
accepted | Fourier Coefficients and Hölder Continuity |
Jan
30 |
comment |
Fourier Coefficients and Hölder Continuity
I'm not sure I understand the notation $\phi_{\nu}(D_x)u$ |
Jan
30 |
comment |
Fourier Coefficients and Hölder Continuity
That is a nice sufficient condition. I own Stein and Shakarchi, as far as I am aware they never tackled such complicated questions, have I skimmed over some section? |
Jan
30 |
comment |
Fourier Coefficients and Hölder Continuity
Yes I used Bernstein's theorem to construct my counterexample above. Do you know of any functions that both satisfy $f\in \mathcal{l}^1(\ZZ)$ and $|\hat{f}(n)|\leq C_f|n|^{-\alpha}$ for some $\alpha>1/2$ but $f$ is not Holder continuous of order $\alpha$. |
Jan
30 |
asked | Fourier Coefficients and Hölder Continuity |
Jan
28 |
awarded | Scholar |
Jan
28 |
awarded | Supporter |
Jan
28 |
comment |
When does continuity imply holomorphy?
Thanks, I'll check those out! |
Jan
28 |
accepted | When does continuity imply holomorphy? |
Jan
28 |
awarded | Student |
Jan
28 |
asked | When does continuity imply holomorphy? |