Elementary problems solved with Functional Analysis
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Many times people come and ask me what Functional Analysis is used for and why it's interesting. Of course interest is a matter of taste, and I for one love the subject as it is. There are far reaching applications to Physics, PDE, other areas of analysis and other advanced subjects that I wouldn't be able to demonstrate say to a first or even second year undergraduate student.
What about examples that can be stated in very simple terms, and are somehow "familiar" to the broader audience? I am not aware of classical or definitive examples, so I wanted to ask:
What are some (preferably mathematical) applications of Functional Analysis, that are as elementary as possible?
real-analysis functional-analysis reference-request soft-question
asked Jan 24 at 18:11
pitariverpitariver
349112
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add a comment |
$begingroup$
Many times people come and ask me what Functional Analysis is used for and why it's interesting. Of course interest is a matter of taste, and I for one love the subject as it is. There are far reaching applications to Physics, PDE, other areas of analysis and other advanced subjects that I wouldn't be able to demonstrate say to a first or even second year undergraduate student.
What about examples that can be stated in very simple terms, and are somehow "familiar" to the broader audience? I am not aware of classical or definitive examples, so I wanted to ask:
What are some (preferably mathematical) applications of Functional Analysis, that are as elementary as possible?
real-analysis functional-analysis reference-request soft-question
asked Jan 24 at 18:11
pitariverpitariver
349112
$endgroup$
$begingroup$
Unfortunately, I don't think this question fits the format of the site - poll questions are explicitly off-topic here.
$endgroup$
– T. Bongers
Jan 24 at 18:17
1
$begingroup$
@T.Bongers Where should I post it then? I have seen several similar well received questions. Would slightly rephrasing the question help?
$endgroup$
– pitariver
Jan 24 at 18:36
$begingroup$
There are plenty of mathematical discussion forums around the internet, but MSE is not one of them. Historically, there were poll-based questions, but they frequently aren't seen as on-topic anymore.
$endgroup$
– T. Bongers
Jan 24 at 19:12
add a comment |
$begingroup$
Many times people come and ask me what Functional Analysis is used for and why it's interesting. Of course interest is a matter of taste, and I for one love the subject as it is. There are far reaching applications to Physics, PDE, other areas of analysis and other advanced subjects that I wouldn't be able to demonstrate say to a first or even second year undergraduate student.
What about examples that can be stated in very simple terms, and are somehow "familiar" to the broader audience? I am not aware of classical or definitive examples, so I wanted to ask:
What are some (preferably mathematical) applications of Functional Analysis, that are as elementary as possible?
real-analysis functional-analysis reference-request soft-question
asked Jan 24 at 18:11
pitariverpitariver
349112
$endgroup$
Many times people come and ask me what Functional Analysis is used for and why it's interesting. Of course interest is a matter of taste, and I for one love the subject as it is. There are far reaching applications to Physics, PDE, other areas of analysis and other advanced subjects that I wouldn't be able to demonstrate say to a first or even second year undergraduate student.
What about examples that can be stated in very simple terms, and are somehow "familiar" to the broader audience? I am not aware of classical or definitive examples, so I wanted to ask:
What are some (preferably mathematical) applications of Functional Analysis, that are as elementary as possible?
real-analysis functional-analysis reference-request soft-question
real-analysis functional-analysis reference-request soft-question
asked Jan 24 at 18:11
pitariverpitariver
349112
asked Jan 24 at 18:11
pitariverpitariver
349112
edited Jan 24 at 19:07
pitariver
asked Jan 24 at 18:11
pitariverpitariver
349112
asked Jan 24 at 18:11
pitariverpitariver
349112
asked Jan 24 at 18:11
pitariverpitariver
349112
349112
$begingroup$
Unfortunately, I don't think this question fits the format of the site - poll questions are explicitly off-topic here.
$endgroup$
– T. Bongers
Jan 24 at 18:17
1
$begingroup$
@T.Bongers Where should I post it then? I have seen several similar well received questions. Would slightly rephrasing the question help?
$endgroup$
– pitariver
Jan 24 at 18:36
$begingroup$
There are plenty of mathematical discussion forums around the internet, but MSE is not one of them. Historically, there were poll-based questions, but they frequently aren't seen as on-topic anymore.
$endgroup$
– T. Bongers
Jan 24 at 19:12
add a comment |
$begingroup$
Unfortunately, I don't think this question fits the format of the site - poll questions are explicitly off-topic here.
$endgroup$
– T. Bongers
Jan 24 at 18:17
1
$begingroup$
@T.Bongers Where should I post it then? I have seen several similar well received questions. Would slightly rephrasing the question help?
$endgroup$
– pitariver
Jan 24 at 18:36
$begingroup$
There are plenty of mathematical discussion forums around the internet, but MSE is not one of them. Historically, there were poll-based questions, but they frequently aren't seen as on-topic anymore.
$endgroup$
– T. Bongers
Jan 24 at 19:12
$begingroup$
Unfortunately, I don't think this question fits the format of the site - poll questions are explicitly off-topic here.
$endgroup$
– T. Bongers
Jan 24 at 18:17
$begingroup$
Unfortunately, I don't think this question fits the format of the site - poll questions are explicitly off-topic here.
$endgroup$
– T. Bongers
Jan 24 at 18:17
1
1
$begingroup$
@T.Bongers Where should I post it then? I have seen several similar well received questions. Would slightly rephrasing the question help?
$endgroup$
– pitariver
Jan 24 at 18:36
$begingroup$
@T.Bongers Where should I post it then? I have seen several similar well received questions. Would slightly rephrasing the question help?
$endgroup$
– pitariver
Jan 24 at 18:36
$begingroup$
There are plenty of mathematical discussion forums around the internet, but MSE is not one of them. Historically, there were poll-based questions, but they frequently aren't seen as on-topic anymore.
$endgroup$
– T. Bongers
Jan 24 at 19:12
$begingroup$
There are plenty of mathematical discussion forums around the internet, but MSE is not one of them. Historically, there were poll-based questions, but they frequently aren't seen as on-topic anymore.
$endgroup$
– T. Bongers
Jan 24 at 19:12
add a comment |
2 Answers
2
active
oldest
votes
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A very important application is data compression, the theory of wavelets being particulary interesting here.
answered Jan 24 at 18:18
José Carlos SantosJosé Carlos Santos
161k22127232
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add a comment |
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My favorite application: Image/video/sound compression and denoising (and more generally, signal processing).
From Fourier to Wavelet decomposition of signals, there is a plethora of techniques stemming from functional analysis for compressing and understanding signals. Examples:
- Fourier analysis is the basis for JPEG compression (everyone knows JPEG, right?).
- Wavelet and Fourier are both used in video compression.
- Fourier is used a lot in sound denoising and filtering.
- etc...
answered Jan 24 at 18:20
Stefan LafonStefan Lafon
1,89618
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add a comment |
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2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
A very important application is data compression, the theory of wavelets being particulary interesting here.
answered Jan 24 at 18:18
José Carlos SantosJosé Carlos Santos
161k22127232
$endgroup$
add a comment |
$begingroup$
A very important application is data compression, the theory of wavelets being particulary interesting here.
answered Jan 24 at 18:18
José Carlos SantosJosé Carlos Santos
161k22127232
$endgroup$
add a comment |
$begingroup$
A very important application is data compression, the theory of wavelets being particulary interesting here.
answered Jan 24 at 18:18
José Carlos SantosJosé Carlos Santos
161k22127232
$endgroup$
A very important application is data compression, the theory of wavelets being particulary interesting here.
answered Jan 24 at 18:18
José Carlos SantosJosé Carlos Santos
161k22127232
answered Jan 24 at 18:18
José Carlos SantosJosé Carlos Santos
161k22127232
answered Jan 24 at 18:18
José Carlos SantosJosé Carlos Santos
161k22127232
answered Jan 24 at 18:18
José Carlos SantosJosé Carlos Santos
161k22127232
161k22127232
add a comment |
add a comment |
$begingroup$
My favorite application: Image/video/sound compression and denoising (and more generally, signal processing).
From Fourier to Wavelet decomposition of signals, there is a plethora of techniques stemming from functional analysis for compressing and understanding signals. Examples:
- Fourier analysis is the basis for JPEG compression (everyone knows JPEG, right?).
- Wavelet and Fourier are both used in video compression.
- Fourier is used a lot in sound denoising and filtering.
- etc...
answered Jan 24 at 18:20
Stefan LafonStefan Lafon
1,89618
$endgroup$
add a comment |
$begingroup$
My favorite application: Image/video/sound compression and denoising (and more generally, signal processing).
From Fourier to Wavelet decomposition of signals, there is a plethora of techniques stemming from functional analysis for compressing and understanding signals. Examples:
- Fourier analysis is the basis for JPEG compression (everyone knows JPEG, right?).
- Wavelet and Fourier are both used in video compression.
- Fourier is used a lot in sound denoising and filtering.
- etc...
answered Jan 24 at 18:20
Stefan LafonStefan Lafon
1,89618
$endgroup$
add a comment |
$begingroup$
My favorite application: Image/video/sound compression and denoising (and more generally, signal processing).
From Fourier to Wavelet decomposition of signals, there is a plethora of techniques stemming from functional analysis for compressing and understanding signals. Examples:
- Fourier analysis is the basis for JPEG compression (everyone knows JPEG, right?).
- Wavelet and Fourier are both used in video compression.
- Fourier is used a lot in sound denoising and filtering.
- etc...
answered Jan 24 at 18:20
Stefan LafonStefan Lafon
1,89618
$endgroup$
My favorite application: Image/video/sound compression and denoising (and more generally, signal processing).
From Fourier to Wavelet decomposition of signals, there is a plethora of techniques stemming from functional analysis for compressing and understanding signals. Examples:
- Fourier analysis is the basis for JPEG compression (everyone knows JPEG, right?).
- Wavelet and Fourier are both used in video compression.
- Fourier is used a lot in sound denoising and filtering.
- etc...
answered Jan 24 at 18:20
Stefan LafonStefan Lafon
1,89618
answered Jan 24 at 18:20
Stefan LafonStefan Lafon
1,89618
answered Jan 24 at 18:20
Stefan LafonStefan Lafon
1,89618
answered Jan 24 at 18:20
Stefan LafonStefan Lafon
1,89618
1,89618
add a comment |
add a comment |
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$begingroup$
Unfortunately, I don't think this question fits the format of the site - poll questions are explicitly off-topic here.
$endgroup$
– T. Bongers
Jan 24 at 18:17
1
$begingroup$
@T.Bongers Where should I post it then? I have seen several similar well received questions. Would slightly rephrasing the question help?
$endgroup$
– pitariver
Jan 24 at 18:36
$begingroup$
There are plenty of mathematical discussion forums around the internet, but MSE is not one of them. Historically, there were poll-based questions, but they frequently aren't seen as on-topic anymore.
$endgroup$
– T. Bongers
Jan 24 at 19:12