Question

Show that $\int_{-\infty}^{\infty}\exp\left({-\left(\sqrt {4\pi^{2} t}\xi+\frac{i(y-x)}{2\sqrt t}~\right)^{2}}\right)\,d\xi =\frac{1}{\sqrt {4\pi t}}$

score 94 · Answer 1 · 2026-03-27 23:23:29

94

Views

Show that $\int_{-\infty}^{\infty}\exp\left({-\left(\sqrt {4\pi^{2} t}\xi+\frac{i(y-x)}{2\sqrt t}~\right)^{2}}\right)\,d\xi =\frac{1}{\sqrt {4\pi t}}$

Published on 27 Mar 2026 - 23:23

score 70 · Answer 2 · 2026-03-24 22:51:09

70

Views

Show that function is Lipschitz continuous at $ x = 0$

Published on 24 Mar 2026 - 22:51

score 90 · Answer 3 · 2026-03-25 13:34:27

90

Views

Paper in Calculus of Variation: Question on why $\;\inf \{ E_1(u)\}\;$ can't be less than $\;\min \{E_1(u)\}\;$

Published on 25 Mar 2026 - 13:34

score 53 · Answer 4 · 2026-04-01 18:11:45

53

Views

Find minimum or lower bound of $f(x)=\int_{B(0,R)}\log(\frac{|x-y|}{|x-\frac{R^2}{||y||^2}y|})dy$

Published on 01 Apr 2026 - 18:11

score 96 · Answer 5 · 2026-03-30 12:31:23

96

Views

Show that for any $E\subseteq X$ we have $f(\overline{E})$ $\subseteq$ $\overline{f(E)}$.

Published on 30 Mar 2026 - 12:31

score 533 · Answer 6 · 2026-03-25 11:15:00

533

Views

The space of convergent sequences is not dual to any space.

Published on 25 Mar 2026 - 11:15

score 50 · Answer 7 · 2026-03-27 13:28:40

50

Views

The problem of the formula of Fourier series

Published on 27 Mar 2026 - 13:28

score 1.3k · Answer 8 · 2018-03-02 10:00:17

1.3k

Views

No Limit Points $\implies$ Countable

Published on 02 Mar 2018 - 10:00

score 24 · Answer 9 · 2018-03-02 16:17:22

24

Views

implications about the existence of limits

Published on 02 Mar 2018 - 16:17

score 339 · Answer 10 · 2026-03-26 19:50:44

339

Views

Compact,connected set

Published on 26 Mar 2026 - 19:50

score 47 · Answer 11 · 2026-03-31 18:00:33

47

Views

New norms on $L^2$

Published on 31 Mar 2026 - 18:00

score 121 · Answer 12 · 2026-04-01 19:36:53

121

Views

How to deal with the partial inverse of a two-variable function?

Published on 01 Apr 2026 - 19:36

score 158 · Answer 13 · 2026-03-28 04:35:41

158

Views

Let $a_n \rightarrow A$ and $b_n \rightarrow B$ as $n \rightarrow \infty$, with $a_n \leq b_n$ for all $n$. Show $A \leq B$.

Published on 28 Mar 2026 - 4:35

score 72 · Answer 14 · 2026-03-28 23:59:46

72

Views

Prove that the series $\sum \frac{a_n}{r_n}$ diverges.

Published on 28 Mar 2026 - 23:59

score 129 · Answer 15 · 2018-03-03 15:35:09

129

Views

Prove that $\{f * \phi _n\}$ uniformly converges to $f$.

Published on 03 Mar 2018 - 15:35

List Question

Show that $\int_{-\infty}^{\infty}\exp\left({-\left(\sqrt {4\pi^{2} t}\xi+\frac{i(y-x)}{2\sqrt t}~\right)^{2}}\right)\,d\xi =\frac{1}{\sqrt {4\pi t}}$

Show that function is Lipschitz continuous at $ x = 0$

Paper in Calculus of Variation: Question on why $\;\inf \{ E_1(u)\}\;$ can't be less than $\;\min \{E_1(u)\}\;$

Find minimum or lower bound of $f(x)=\int_{B(0,R)}\log(\frac{|x-y|}{|x-\frac{R^2}{||y||^2}y|})dy$

Show that for any $E\subseteq X$ we have $f(\overline{E})$ $\subseteq$ $\overline{f(E)}$.

The space of convergent sequences is not dual to any space.

The problem of the formula of Fourier series

No Limit Points $\implies$ Countable

implications about the existence of limits

Compact,connected set

New norms on $L^2$

How to deal with the partial inverse of a two-variable function?

Let $a_n \rightarrow A$ and $b_n \rightarrow B$ as $n \rightarrow \infty$, with $a_n \leq b_n$ for all $n$. Show $A \leq B$.

Prove that the series $\sum \frac{a_n}{r_n}$ diverges.

Prove that $\{f * \phi _n\}$ uniformly converges to $f$.

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