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Results tagged with measure-theory
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user 4519
Questions about abstract measure and Lebesgue integral theory. Also concerns such properties as measurability of maps and sets.
8
votes
2
answers
3k
views
Is $f(x,y)=\sum_{n\in\mathbb{Z}\backslash\{0\}}\frac{1}{n}e^{2\pi i(xn+yn^2)}$ essentially b...
Let $$f(x,y)=\sum_{n\in\mathbb{Z}\backslash\{0\}}\frac{1}{n}e^{2\pi i(xn+yn^2)}
$$
Is it true that $\|f\|_{L^{\infty}(\mathbb{R}^2)}<\infty$? i.e. is $f$ essentially bounded?
- 463
5
votes
Is $f(x,y)=\sum_{n\in\mathbb{Z}\backslash\{0\}}\frac{1}{n}e^{2\pi i(xn+yn^2)}$ essentially b...
Prof. Tao's answer is excellent. I also found two research papers answering the question so I list them below as complementary reference:
G.I.Arkhipov and K.I.Oskolkov, On a special trigonometric se …
- 463