Jean Bourgain's Relatively Lesser Known Significant Contributions
A great mathematician is no longer with us.
Terry Tao has blogged about Bourgain's death and mentioned some of his more recent significant contributions, such as the proof of Vinogradov's conjecture with Guth and Demeter. He was of course very prolific and his work spanned many areas. There are a few questions at mathoverflow (e.g., here and here) regarding his technical contributions.
I am sure there are some of his contributions that may not be as widely known, but deserve to be so. Perhaps focusing on results with unexpected aplications may be a good start, but any answers are welcome.
I was unable to find the list of talks at the conference in his honour at the IAS mentioned and linked to in Tao's post, but that may be just me.
Thanks to Josiah Park for pointing out the link to the IAS Bourgain conference, titled 'Analysis and Beyond'. In fact, the videos of the talks are also there.
nt.number-theory fa.functional-analysis ho.history-overview fourier-analysis additive-combinatorics
add a comment |
A great mathematician is no longer with us.
Terry Tao has blogged about Bourgain's death and mentioned some of his more recent significant contributions, such as the proof of Vinogradov's conjecture with Guth and Demeter. He was of course very prolific and his work spanned many areas. There are a few questions at mathoverflow (e.g., here and here) regarding his technical contributions.
I am sure there are some of his contributions that may not be as widely known, but deserve to be so. Perhaps focusing on results with unexpected aplications may be a good start, but any answers are welcome.
I was unable to find the list of talks at the conference in his honour at the IAS mentioned and linked to in Tao's post, but that may be just me.
Thanks to Josiah Park for pointing out the link to the IAS Bourgain conference, titled 'Analysis and Beyond'. In fact, the videos of the talks are also there.
nt.number-theory fa.functional-analysis ho.history-overview fourier-analysis additive-combinatorics
The list of talks appears to be here: math.ias.edu/bourgain16/schedule
– Josiah Park
6 hours ago
@JosiahPark, thanks that's great.
– kodlu
6 hours ago
add a comment |
A great mathematician is no longer with us.
Terry Tao has blogged about Bourgain's death and mentioned some of his more recent significant contributions, such as the proof of Vinogradov's conjecture with Guth and Demeter. He was of course very prolific and his work spanned many areas. There are a few questions at mathoverflow (e.g., here and here) regarding his technical contributions.
I am sure there are some of his contributions that may not be as widely known, but deserve to be so. Perhaps focusing on results with unexpected aplications may be a good start, but any answers are welcome.
I was unable to find the list of talks at the conference in his honour at the IAS mentioned and linked to in Tao's post, but that may be just me.
Thanks to Josiah Park for pointing out the link to the IAS Bourgain conference, titled 'Analysis and Beyond'. In fact, the videos of the talks are also there.
nt.number-theory fa.functional-analysis ho.history-overview fourier-analysis additive-combinatorics
A great mathematician is no longer with us.
Terry Tao has blogged about Bourgain's death and mentioned some of his more recent significant contributions, such as the proof of Vinogradov's conjecture with Guth and Demeter. He was of course very prolific and his work spanned many areas. There are a few questions at mathoverflow (e.g., here and here) regarding his technical contributions.
I am sure there are some of his contributions that may not be as widely known, but deserve to be so. Perhaps focusing on results with unexpected aplications may be a good start, but any answers are welcome.
I was unable to find the list of talks at the conference in his honour at the IAS mentioned and linked to in Tao's post, but that may be just me.
Thanks to Josiah Park for pointing out the link to the IAS Bourgain conference, titled 'Analysis and Beyond'. In fact, the videos of the talks are also there.
nt.number-theory fa.functional-analysis ho.history-overview fourier-analysis additive-combinatorics
nt.number-theory fa.functional-analysis ho.history-overview fourier-analysis additive-combinatorics
edited 1 hour ago
community wiki
5 revs, 3 users 60%
kodlu
The list of talks appears to be here: math.ias.edu/bourgain16/schedule
– Josiah Park
6 hours ago
@JosiahPark, thanks that's great.
– kodlu
6 hours ago
add a comment |
The list of talks appears to be here: math.ias.edu/bourgain16/schedule
– Josiah Park
6 hours ago
@JosiahPark, thanks that's great.
– kodlu
6 hours ago
The list of talks appears to be here: math.ias.edu/bourgain16/schedule
– Josiah Park
6 hours ago
The list of talks appears to be here: math.ias.edu/bourgain16/schedule
– Josiah Park
6 hours ago
@JosiahPark, thanks that's great.
– kodlu
6 hours ago
@JosiahPark, thanks that's great.
– kodlu
6 hours ago
add a comment |
1 Answer
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It follows from results in Bourgain's Acta 1984 paper (but I have the impression these results were announced some years ealier?) that the dual of the disc algebra $A({bf D})$ has cotype 2; and every bounded linear map from $A({bf D})$ to a Banach space of cotype 2 is 2-summing. As a corollary, the canonical injection $A({bf D}) hatotimes A({bf D}) to C({bf T})hatotimes C({bf T})$ has closed range. (See this MO question for my attempt to find out if this holds for any other examples of uniform algebras.)
These results are sometimes packaged together under the description "Grothendieck's inequality holds for the disc algebra", the point being that the Grothendieck's inequality can be interpreted as a statement about bounded bilinear maps on $C(K)$-spaces, and one doesn't expect proper uniform algebras to have all the nice Banach-space properties that $C(K)$-spaces do.
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1 Answer
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1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
It follows from results in Bourgain's Acta 1984 paper (but I have the impression these results were announced some years ealier?) that the dual of the disc algebra $A({bf D})$ has cotype 2; and every bounded linear map from $A({bf D})$ to a Banach space of cotype 2 is 2-summing. As a corollary, the canonical injection $A({bf D}) hatotimes A({bf D}) to C({bf T})hatotimes C({bf T})$ has closed range. (See this MO question for my attempt to find out if this holds for any other examples of uniform algebras.)
These results are sometimes packaged together under the description "Grothendieck's inequality holds for the disc algebra", the point being that the Grothendieck's inequality can be interpreted as a statement about bounded bilinear maps on $C(K)$-spaces, and one doesn't expect proper uniform algebras to have all the nice Banach-space properties that $C(K)$-spaces do.
add a comment |
It follows from results in Bourgain's Acta 1984 paper (but I have the impression these results were announced some years ealier?) that the dual of the disc algebra $A({bf D})$ has cotype 2; and every bounded linear map from $A({bf D})$ to a Banach space of cotype 2 is 2-summing. As a corollary, the canonical injection $A({bf D}) hatotimes A({bf D}) to C({bf T})hatotimes C({bf T})$ has closed range. (See this MO question for my attempt to find out if this holds for any other examples of uniform algebras.)
These results are sometimes packaged together under the description "Grothendieck's inequality holds for the disc algebra", the point being that the Grothendieck's inequality can be interpreted as a statement about bounded bilinear maps on $C(K)$-spaces, and one doesn't expect proper uniform algebras to have all the nice Banach-space properties that $C(K)$-spaces do.
add a comment |
It follows from results in Bourgain's Acta 1984 paper (but I have the impression these results were announced some years ealier?) that the dual of the disc algebra $A({bf D})$ has cotype 2; and every bounded linear map from $A({bf D})$ to a Banach space of cotype 2 is 2-summing. As a corollary, the canonical injection $A({bf D}) hatotimes A({bf D}) to C({bf T})hatotimes C({bf T})$ has closed range. (See this MO question for my attempt to find out if this holds for any other examples of uniform algebras.)
These results are sometimes packaged together under the description "Grothendieck's inequality holds for the disc algebra", the point being that the Grothendieck's inequality can be interpreted as a statement about bounded bilinear maps on $C(K)$-spaces, and one doesn't expect proper uniform algebras to have all the nice Banach-space properties that $C(K)$-spaces do.
It follows from results in Bourgain's Acta 1984 paper (but I have the impression these results were announced some years ealier?) that the dual of the disc algebra $A({bf D})$ has cotype 2; and every bounded linear map from $A({bf D})$ to a Banach space of cotype 2 is 2-summing. As a corollary, the canonical injection $A({bf D}) hatotimes A({bf D}) to C({bf T})hatotimes C({bf T})$ has closed range. (See this MO question for my attempt to find out if this holds for any other examples of uniform algebras.)
These results are sometimes packaged together under the description "Grothendieck's inequality holds for the disc algebra", the point being that the Grothendieck's inequality can be interpreted as a statement about bounded bilinear maps on $C(K)$-spaces, and one doesn't expect proper uniform algebras to have all the nice Banach-space properties that $C(K)$-spaces do.
answered 2 hours ago
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Yemon Choi
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The list of talks appears to be here: math.ias.edu/bourgain16/schedule
– Josiah Park
6 hours ago
@JosiahPark, thanks that's great.
– kodlu
6 hours ago