How does the locally compact group play a role in many branches of math? [closed]
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It seems that Fourier analysis/harmonic analysis plays an important role in math, at least in number theory and statistics. It also seems to me that talking about it is talking about locally compact groups. So to have a big picture, can you explain to me how the local and non-local compact, compact and non-compact groups play a role in many branches of math?
I'm looking for an answer similarly to the one in What does $S^1$ do in many branches of math? My background is Dym & McKean, Fourier Series and Integrals. I still don't understand much what that group mean though.
math-history harmonic-analysis big-list locally-compact-groups big-picture
asked Nov 12 at 14:56
Ooker
314318
closed as too broad by Trevor Gunn, Lord Shark the Unknown, amWhy, hardmath, Shailesh Nov 17 at 0:03
Please edit the question to limit it to a specific problem with enough detail to identify an adequate answer. Avoid asking multiple distinct questions at once. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
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up vote
1
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It seems that Fourier analysis/harmonic analysis plays an important role in math, at least in number theory and statistics. It also seems to me that talking about it is talking about locally compact groups. So to have a big picture, can you explain to me how the local and non-local compact, compact and non-compact groups play a role in many branches of math?
I'm looking for an answer similarly to the one in What does $S^1$ do in many branches of math? My background is Dym & McKean, Fourier Series and Integrals. I still don't understand much what that group mean though.
math-history harmonic-analysis big-list locally-compact-groups big-picture
asked Nov 12 at 14:56
Ooker
314318
closed as too broad by Trevor Gunn, Lord Shark the Unknown, amWhy, hardmath, Shailesh Nov 17 at 0:03
Please edit the question to limit it to a specific problem with enough detail to identify an adequate answer. Avoid asking multiple distinct questions at once. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
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The scope of your Question could be narrowed. Evidently you are interested not only in locally compact groups, but in topological(?) groups and their applications generally, but such a broad topic is a poor fit for the Math.SE format.
– hardmath
Nov 16 at 17:42
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up vote
1
down vote
favorite
up vote
1
down vote
favorite
It seems that Fourier analysis/harmonic analysis plays an important role in math, at least in number theory and statistics. It also seems to me that talking about it is talking about locally compact groups. So to have a big picture, can you explain to me how the local and non-local compact, compact and non-compact groups play a role in many branches of math?
I'm looking for an answer similarly to the one in What does $S^1$ do in many branches of math? My background is Dym & McKean, Fourier Series and Integrals. I still don't understand much what that group mean though.
math-history harmonic-analysis big-list locally-compact-groups big-picture
asked Nov 12 at 14:56
Ooker
314318
It seems that Fourier analysis/harmonic analysis plays an important role in math, at least in number theory and statistics. It also seems to me that talking about it is talking about locally compact groups. So to have a big picture, can you explain to me how the local and non-local compact, compact and non-compact groups play a role in many branches of math?
I'm looking for an answer similarly to the one in What does $S^1$ do in many branches of math? My background is Dym & McKean, Fourier Series and Integrals. I still don't understand much what that group mean though.
math-history harmonic-analysis big-list locally-compact-groups big-picture
math-history harmonic-analysis big-list locally-compact-groups big-picture
asked Nov 12 at 14:56
Ooker
314318
asked Nov 12 at 14:56
Ooker
314318
edited Nov 16 at 18:21
asked Nov 12 at 14:56
Ooker
314318
asked Nov 12 at 14:56
Ooker
314318
asked Nov 12 at 14:56
Ooker
314318
314318
closed as too broad by Trevor Gunn, Lord Shark the Unknown, amWhy, hardmath, Shailesh Nov 17 at 0:03
Please edit the question to limit it to a specific problem with enough detail to identify an adequate answer. Avoid asking multiple distinct questions at once. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
closed as too broad by Trevor Gunn, Lord Shark the Unknown, amWhy, hardmath, Shailesh Nov 17 at 0:03
Please edit the question to limit it to a specific problem with enough detail to identify an adequate answer. Avoid asking multiple distinct questions at once. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
2
The scope of your Question could be narrowed. Evidently you are interested not only in locally compact groups, but in topological(?) groups and their applications generally, but such a broad topic is a poor fit for the Math.SE format.
– hardmath
Nov 16 at 17:42
add a comment |
2
The scope of your Question could be narrowed. Evidently you are interested not only in locally compact groups, but in topological(?) groups and their applications generally, but such a broad topic is a poor fit for the Math.SE format.
– hardmath
Nov 16 at 17:42
2
2
The scope of your Question could be narrowed. Evidently you are interested not only in locally compact groups, but in topological(?) groups and their applications generally, but such a broad topic is a poor fit for the Math.SE format.
– hardmath
Nov 16 at 17:42
The scope of your Question could be narrowed. Evidently you are interested not only in locally compact groups, but in topological(?) groups and their applications generally, but such a broad topic is a poor fit for the Math.SE format.
– hardmath
Nov 16 at 17:42
add a comment |
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The scope of your Question could be narrowed. Evidently you are interested not only in locally compact groups, but in topological(?) groups and their applications generally, but such a broad topic is a poor fit for the Math.SE format.
– hardmath
Nov 16 at 17:42