Question

Determining uniform convergence of a sequence of exponential functions

score 43 · Answer 1 · 2018-12-13 17:18:32

Determining uniform convergence of a sequence of exponential functions

Published on 13 Dec 2018 - 17:18

score 64 · Answer 2 · 2018-12-14 01:02:08

Suppose we have continuous $f_{n} : D \rightarrow \mathbb{R}$ converging to $f : D \rightarrow \mathbb{R}$ uniformly on $D$. Then, is $f$ continuous?

score 37 · Answer 3 · 2026-02-23 10:22:05

37

Views

Is $f_{n}$ is analytic on $(a, b)$ and $f_{n} \rightarrow f$ uniformly on $(a, b)$ then is $f$ analytic on $(a, b)$?

Published on 23 Feb 2026 - 10:22

score 331 · Answer 4 · 2018-12-14 20:27:35

331

Views

Is $\sum _{n=1} ^ \infty \frac{1}{(x+\pi)^2 \cdot n^2 }$ uniformly convergent on $(-\pi , \pi)$?

Published on 14 Dec 2018 - 20:27

score 1.2k · Answer 5 · 2018-12-15 02:08:04

1.2k

Views

Using proof by contradiction to prove Dini's theorem

Published on 15 Dec 2018 - 2:08

score 242 · Answer 6 · 2018-12-17 12:25:16

242

Views

If a series of functions satisfies the Cauchy criterion uniformly, then the series converges uniformly on $S$

Published on 17 Dec 2018 - 12:25

score 170 · Answer 7 · 2018-12-17 21:22:23

170

Views

Uniform convergence exercise

Published on 17 Dec 2018 - 21:22

score 1.3k · Answer 8 · 2018-12-17 21:31:52

1.3k

Views

Uniform convergence of the exponential series on a bounded interval

Published on 17 Dec 2018 - 21:31

score 65 · Answer 9 · 2026-03-27 04:38:24

65

Views

Uniform Continuity of sum of a series of functions

Published on 27 Mar 2026 - 4:38

score 1k · Answer 10 · 2026-02-23 10:20:32

1k

Views

Uniform convergence of $f_n(x) = \sqrt{x^2 + \frac{1}{n^2}}$, solution verification

Published on 23 Feb 2026 - 10:20

score 1.7k · Answer 11 · 2018-12-19 06:24:29

1.7k

Views

Uniform convergence of $f_n(x)=\frac{\sqrt{1+{(nx)}^2}}{n}$ and ${f_n}^\prime$

Published on 19 Dec 2018 - 6:24

score 210 · Answer 12 · 2026-02-23 01:23:34

210

Views

An extension of a corollary of the Arzela-Ascoli theorem for smooth functions

Published on 23 Feb 2026 - 1:23

score 38 · Answer 13 · 2026-03-23 14:59:49

38

Views

In functional analysis, is there a commonly accepted short-hand notation for specific types of convergence?

Published on 23 Mar 2026 - 14:59

score 96 · Answer 14 · 2026-03-25 15:42:32

96

Views

Hint requested for: If $\sum_{n=0}^{\infty} a_n x^n$ converges for some $x_0$, then it converges uniformly and absolutely on $[-a, a]$ with $a<|x_0|$?

Published on 25 Mar 2026 - 15:42

score 1.1k · Answer 15 · 2018-12-28 20:21:33

1.1k

Views

Let $f : \mathbb{R} \to \mathbb{R}$ be approximated arbitrarily well by polynomials of bounded degree. Prove $f$ is a polynomial.

Published on 28 Dec 2018 - 20:21

List Question

Determining uniform convergence of a sequence of exponential functions

Suppose we have continuous $f_{n} : D \rightarrow \mathbb{R}$ converging to $f : D \rightarrow \mathbb{R}$ uniformly on $D$. Then, is $f$ continuous?

Is $f_{n}$ is analytic on $(a, b)$ and $f_{n} \rightarrow f$ uniformly on $(a, b)$ then is $f$ analytic on $(a, b)$?

Is $\sum _{n=1} ^ \infty \frac{1}{(x+\pi)^2 \cdot n^2 }$ uniformly convergent on $(-\pi , \pi)$?

Using proof by contradiction to prove Dini's theorem

If a series of functions satisfies the Cauchy criterion uniformly, then the series converges uniformly on $S$

Uniform convergence exercise

Uniform convergence of the exponential series on a bounded interval

Uniform Continuity of sum of a series of functions

Uniform convergence of $f_n(x) = \sqrt{x^2 + \frac{1}{n^2}}$, solution verification

Uniform convergence of $f_n(x)=\frac{\sqrt{1+{(nx)}^2}}{n}$ and ${f_n}^\prime$

An extension of a corollary of the Arzela-Ascoli theorem for smooth functions

In functional analysis, is there a commonly accepted short-hand notation for specific types of convergence?

Hint requested for: If $\sum_{n=0}^{\infty} a_n x^n$ converges for some $x_0$, then it converges uniformly and absolutely on $[-a, a]$ with $a<|x_0|$?

Let $f : \mathbb{R} \to \mathbb{R}$ be approximated arbitrarily well by polynomials of bounded degree. Prove $f$ is a polynomial.

Trending Questions

Popular # Hahtags

Popular Questions