Question

under which conditions $\lim_{t\to \infty} \frac{1}{t}\int_0^t f(s)ds$ implies $\lim_{t\to \infty} f(t) $

score 208 · Answer 1 · 2024-02-02 18:54:42

208

Views

under which conditions $\lim_{t\to \infty} \frac{1}{t}\int_0^t f(s)ds$ implies $\lim_{t\to \infty} f(t) $

Published on 02 Feb 2024 - 18:54

score 24 · Answer 2 · 2024-02-03 13:53:08

24

Views

If $f$ is analytic on $B(z_0, R)$, does that imply $f$ has a power series expansion centered at $z_0$ with radius of convergence $R$?

Published on 03 Feb 2024 - 13:53

score 95 · Answer 3 · 2026-03-26 07:59:11

95

Views

Computing the domain of analyticity of $f(z)=\sqrt{z^2-1}$

Published on 26 Mar 2026 - 7:59

score 81 · Answer 4 · 2024-02-06 00:39:08

81

Views

Meaning of "$f$ has a power series expansion around $p$"

Published on 06 Feb 2024 - 0:39

score 17 · Answer 5 · 2026-02-23 10:45:13

17

Views

Characterizing the unimodular functions from the closed disk $\mathbb{C}$ to $\mathbb{C}$ with constraints

Published on 23 Feb 2026 - 10:45

score 42 · Answer 6 · 2026-03-28 04:35:15

42

Views

Analytically continuing a function of two complex variables.

Published on 28 Mar 2026 - 4:35

score 37 · Answer 7 · 2024-02-17 11:54:35

37

Views

$f=\phi(v)+\textbf i v$ is analytic, prove that $f$ is constant

Published on 17 Feb 2024 - 11:54

score 42 · Answer 8 · 2026-03-26 11:03:43

42

Views

How to test if a certain differential equation has an analytic solution (solution has Taylor expansion)?

Published on 26 Mar 2026 - 11:03

score 44 · Answer 9 · 2024-02-21 17:53:12

44

Views

Radius of convergence of a power series defined in terms of co-efficients around another point

Published on 21 Feb 2024 - 17:53

score 77 · Answer 10 · 2024-02-22 01:33:14

77

Views

If an analytic function is identically zero in a domain, can it be always divided by another analytic function in that domain?

Published on 22 Feb 2024 - 1:33

score 122 · Answer 11 · 2024-02-23 06:02:47

122

Views

Proving that $f$ is rational if it is known that $f$ is analytic in $\mathbb{D}$ and satisfies $|f(z)| \to 1$ as $|z| \to 1$

Published on 23 Feb 2024 - 6:02

score 30 · Answer 12 · 2024-02-23 21:40:55

30

Views

Real analytic function on $X$ is subanalytic on compact subsets $Q\subseteq X$.

Published on 23 Feb 2024 - 21:40

score 30 · Answer 13 · 2024-02-24 17:08:07

30

Views

Decomposition of analytic functions on the upper half plane

Published on 24 Feb 2024 - 17:08

score 67 · Answer 14 · 2026-03-26 12:40:30

67

Views

Smooth Riemannian metric is locally real analytic?

Published on 26 Mar 2026 - 12:40

score 40 · Answer 15 · 2024-03-02 18:26:47

40

Views

Can we write every $C^1$ complex function on the unit circle as the the difference of two approriate functions?

Published on 02 Mar 2024 - 18:26

List Question

under which conditions $\lim_{t\to \infty} \frac{1}{t}\int_0^t f(s)ds$ implies $\lim_{t\to \infty} f(t) $

If $f$ is analytic on $B(z_0, R)$, does that imply $f$ has a power series expansion centered at $z_0$ with radius of convergence $R$?

Computing the domain of analyticity of $f(z)=\sqrt{z^2-1}$

Meaning of "$f$ has a power series expansion around $p$"

Characterizing the unimodular functions from the closed disk $\mathbb{C}$ to $\mathbb{C}$ with constraints

Analytically continuing a function of two complex variables.

$f=\phi(v)+\textbf i v$ is analytic, prove that $f$ is constant

How to test if a certain differential equation has an analytic solution (solution has Taylor expansion)?

Radius of convergence of a power series defined in terms of co-efficients around another point

If an analytic function is identically zero in a domain, can it be always divided by another analytic function in that domain?

Proving that $f$ is rational if it is known that $f$ is analytic in $\mathbb{D}$ and satisfies $|f(z)| \to 1$ as $|z| \to 1$

Real analytic function on $X$ is subanalytic on compact subsets $Q\subseteq X$.

Decomposition of analytic functions on the upper half plane

Smooth Riemannian metric is locally real analytic?

Can we write every $C^1$ complex function on the unit circle as the the difference of two approriate functions?

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