is H_s an algebra?
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From: Joubert on 19 Jun 2010 06:48 Is it true that given f,g in H_s (s real and s > n/2) and indicating with F the Fourier transform operator we have: F(fg) = F(f)*F(g) ? In other words is H_s an algebra for s > n/2 ? I hope I'm making some sense. Any approachable reference on Sobolev spaces? My notes are a disaster, even online notes are fine. Thanks in advance
From: Bastian Erdnuess on 19 Jun 2010 22:14 Did you solved your question? Joubert wrote: > Is it true that given f,g in H_s (s real and s > n/2) and indicating > with F the Fourier transform operator we have: > > F(fg) = F(f)*F(g) ? > > In other words is H_s an algebra for s > n/2 ? How would this make H_s to an algebra? > I hope I'm making some sense. > Any approachable reference on Sobolev spaces? > My notes are a disaster, even online notes are fine. Do you want to know if H_s is closed under convolution? Or do you want to know something about the Fourier transform on H_s? Cheers Bastian
From: Joubert on 19 Jun 2010 22:18 > How would this make H_s to an algebra? > Good question. Is H_s an algebra in any way? > Do you want to know if H_s is closed under convolution? Or do you want > to know something about the Fourier transform on H_s? Both would help. Like I said the notes I have are almost unreadable and clearly taken without respecting any logical consecutio, so all I can grasp is an outline of the topics.
From: Bastian Erdnuess on 19 Jun 2010 22:51 Joubert wrote: >> How would this make H_s to an algebra? > > Good question. Is H_s an algebra in any way? Sure, in many ways. H_s is e.g. a IR vector space with the pointwise addition (modulus equivalence classes on H_s) and with the pointwise multiplication you get an IR algebra. But I doubt that's your answer. >> Do you want to know if H_s is closed under convolution? Or do you want >> to know something about the Fourier transform on H_s? > > Both would help. Like I said the notes I have are almost unreadable and > clearly taken without respecting any logical consecutio, so all I can > grasp is an outline of the topics. Who did the notes? Why are you interested in them? You could try to post the outline of the topics and hope that someone can give you a clue for a good book about them. Cheers Bastian
From: A N Niel on 20 Jun 2010 07:46 In article <slrni1r0h1.2nm.earthnut(a)wh36-e604.wh36.uni-karlsruhe.de>, Bastian Erdnuess <earthnut(a)web.de> wrote: > Joubert wrote: > > >> How would this make H_s to an algebra? > > > > Good question. Is H_s an algebra in any way? > > Sure, in many ways. H_s is e.g. a IR vector space with the pointwise > addition (modulus equivalence classes on H_s) and with the pointwise > multiplication you get an IR algebra. Not unless the product of two H_s functions is again an H_s function. And if true, that would answer the question. > But I doubt that's your answer. > > >> Do you want to know if H_s is closed under convolution? Or do you want > >> to know something about the Fourier transform on H_s? > > > > Both would help. Like I said the notes I have are almost unreadable and > > clearly taken without respecting any logical consecutio, so all I can > > grasp is an outline of the topics. > > Who did the notes? Why are you interested in them? You could try to > post the outline of the topics and hope that someone can give you a clue > for a good book about them. > > Cheers > Bastian
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