List questions from arzela-ascoli

223

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Is the integral operator $I: L^1([0,1])\to L^1([0,1]), f\mapsto (x\mapsto \int_0^x f \,\mathrm d\lambda)$ compact?

Published on 28 Dec 2021 - 17:31

286

Views

Arzelà–Ascoli $\implies$ Dini's theorem

Published on 30 Dec 2021 - 10:44

133

Views

Variation of Ascoli-Arzelà theorem for $C^1$ functions

Published on 04 Jan 2022 - 20:15

523

Views

Sequence of contraction mapping and convergence of fixed point

Published on 05 Jan 2022 - 9:34

154

Views

A version of Ascoli-Arzelà using modulus of continuity and nth entropy numbers

Published on 10 Jan 2022 - 6:33

60

Views

Solution verification of a proof of the Peano existence theorem, using Arzela-Ascoli

Published on 19 Jan 2022 - 10:07

59

Views

Extraction of pointwise convergenct subsequence using Arzela-Ascoli theorem

Published on 17 Feb 2022 - 17:36

622

Views

When is the compact-open topology locally compact?

Published on 24 Feb 2022 - 22:13

76

Views

Proved that the given set is not closed in the function space $\mathcal{C}([0,1])$

Published on 05 Mar 2022 - 9:25

183

Views

Set of functions with same Lipschitz constant attains a maximum

Published on 20 Mar 2022 - 19:38

50

Views

When is the compact-open topology on homomorphisms locally compact?

Published on 21 Mar 2022 - 1:22

149

Views

Uniform convergence via Arzela-Ascoli

Published on 03 May 2022 - 6:17

27

Views

Check the definition of "pointwise bounded under $d$"

Published on 04 May 2022 - 14:11

174

Views

Space of Lipschitz functions is finite dimensional

Published on 29 May 2022 - 4:24

62

Views

Arzelà–Ascoli propagation theorem

Published on 17 Jun 2022 - 0:56

List Question

Is the integral operator $I: L^1([0,1])\to L^1([0,1]), f\mapsto (x\mapsto \int_0^x f \,\mathrm d\lambda)$ compact?

Arzelà–Ascoli $\implies$ Dini's theorem

Variation of Ascoli-Arzelà theorem for $C^1$ functions

Sequence of contraction mapping and convergence of fixed point

A version of Ascoli-Arzelà using modulus of continuity and nth entropy numbers

Solution verification of a proof of the Peano existence theorem, using Arzela-Ascoli

Extraction of pointwise convergenct subsequence using Arzela-Ascoli theorem

When is the compact-open topology locally compact?

Proved that the given set is not closed in the function space $\mathcal{C}([0,1])$

Set of functions with same Lipschitz constant attains a maximum

When is the compact-open topology on homomorphisms locally compact?

Uniform convergence via Arzela-Ascoli

Check the definition of "pointwise bounded under $d$"

Space of Lipschitz functions is finite dimensional

Arzelà–Ascoli propagation theorem

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