Question

Non constant and bounded discrite harmonic function

score 151 · Answer 1 · 2023-01-03 14:48:56

151

Views

Non constant and bounded discrite harmonic function

Published on 03 Jan 2023 - 14:48

score 152 · Answer 2 · 2023-01-03 17:48:33

152

Views

Bounded functions $f:\mathbb Z^n\to \mathbb R$ that are Discrete Harmonic at all but finite set of points .

Published on 03 Jan 2023 - 17:48

score 152 · Answer 3 · 2023-01-03 19:12:53

152

Views

Dimension of the space of discrete harmonic functions $f:\mathbb Z^n\to \mathbb R$

Published on 03 Jan 2023 - 19:12

score 71 · Answer 4 · 2023-01-04 05:18:35

71

Views

Discrete harmonic functions bounded from below.

Published on 04 Jan 2023 - 5:18

score 241 · Answer 5 · 2023-01-04 18:07:16

241

Views

Are all discrete harmonic function $f:\mathbb Z^2\to \mathbb R$ with less than exponential growth polynomials?

Published on 04 Jan 2023 - 18:07

score 196 · Answer 6 · 2023-01-08 23:45:53

196

Views

A harmonic function on a domain $D$ is infinitely differentiable on $D$

Published on 08 Jan 2023 - 23:45

score 61 · Answer 7 · 2023-01-11 09:55:27

61

Views

Construction of subharmonic function that goes to $-\infty$ on a measurable subset of the boundary

Published on 11 Jan 2023 - 9:55

score 98 · Answer 8 · 2023-01-11 14:20:27

98

Views

Radial limit of Poisson integral equals to the average of the limits from each side.

Published on 11 Jan 2023 - 14:20

score 44 · Answer 9 · 2023-01-11 18:58:50

44

Views

Show that $\lim_{\epsilon\to 0}{A_{\epsilon}(x_0,y_0) - u(x_0,y_0)\over\epsilon^2} = {1\over 4}\Delta u(x_0,y_0)$

Published on 11 Jan 2023 - 18:58

score 120 · Answer 10 · 2023-01-12 09:08:17

120

Views

if $u$ is harmonic on a closed disk around $(x_0,y_0)$ with radius $r$ then it holds the mean value theorem

Published on 12 Jan 2023 - 9:08

score 108 · Answer 11 · 2023-01-12 09:24:53

108

Views

If $u(x,y)$ is harmonic on a domain $D$ and has a global maximum on $D$ then $u$ is constant on $D$

Published on 12 Jan 2023 - 9:24

score 67 · Answer 12 · 2026-03-30 11:54:20

67

Views

Harmonic function and complex analysis can't prove a result.

Published on 30 Mar 2026 - 11:54

score 111 · Answer 13 · 2023-01-14 06:09:47

111

Views

Representation of harmonic function as a series

Published on 14 Jan 2023 - 6:09

score 92 · Answer 14 · 2023-01-20 21:24:54

92

Views

Justifying integration by parts for the convolution of Poisson kernel and a measure

Published on 20 Jan 2023 - 21:24

List Question

Non constant and bounded discrite harmonic function

Bounded functions $f:\mathbb Z^n\to \mathbb R$ that are Discrete Harmonic at all but finite set of points .

Dimension of the space of discrete harmonic functions $f:\mathbb Z^n\to \mathbb R$

Discrete harmonic functions bounded from below.

Are all discrete harmonic function $f:\mathbb Z^2\to \mathbb R$ with less than exponential growth polynomials?

A harmonic function on a domain $D$ is infinitely differentiable on $D$

Construction of subharmonic function that goes to $-\infty$ on a measurable subset of the boundary

Radial limit of Poisson integral equals to the average of the limits from each side.

Show that $\lim_{\epsilon\to 0}{A_{\epsilon}(x_0,y_0) - u(x_0,y_0)\over\epsilon^2} = {1\over 4}\Delta u(x_0,y_0)$

if $u$ is harmonic on a closed disk around $(x_0,y_0)$ with radius $r$ then it holds the mean value theorem

If $u(x,y)$ is harmonic on a domain $D$ and has a global maximum on $D$ then $u$ is constant on $D$

Harmonic function and complex analysis can't prove a result.

Representation of harmonic function as a series

Justifying integration by parts for the convolution of Poisson kernel and a measure

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