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A question on the Non-degenerated bilinear form

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0

$begingroup$

Prove that $<C(G), C(G)>$ is dual system with bilinear form $$int_G phi(x)psi(x)dx $$ and $psi(x),psi(x)in C(G)$

so here i was trying bilinear form im not getting how to prove non-degenerate

definition of the non-degenerate bilinear form is in Linear Integral Equations
By Raimer Kress

linear-algebra operator-theory hilbert-spaces

share|cite|improve this question

asked Mar 15 at 13:53

Inverse ProblemInverse Problem

1,009918

$endgroup$

migrated from mathoverflow.net Mar 15 at 18:21

This question came from our site for professional mathematicians.

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  what is $G$ here ?
  $endgroup$
  – Phil-W
  Mar 17 at 4:37
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @Phil-W,,,measurable set
  $endgroup$
  – Inverse Problem
  Mar 17 at 15:11
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  I'm guessing it's more than that, since you write C(G), you probably mean continuous functions on G right? So it has to be at least a topological space ?
  $endgroup$
  – Phil-W
  Mar 17 at 19:32
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @Phil-W...offcurse G is compact mesuarble and C is continuous fucntions on G
  $endgroup$
  – Inverse Problem
  Mar 18 at 7:11
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  It would help people to help you if you give all the hypothesis you are considering here, and also the notations, and not let them be forced to guess what you mean. For instance, do you suppose that the measure on $G$ is Radon ?
  $endgroup$
  – Phil-W
  Mar 19 at 20:06
  

  
  
  
  

add a comment | 

0

$begingroup$

Prove that $<C(G), C(G)>$ is dual system with bilinear form $$int_G phi(x)psi(x)dx $$ and $psi(x),psi(x)in C(G)$

so here i was trying bilinear form im not getting how to prove non-degenerate

definition of the non-degenerate bilinear form is in Linear Integral Equations
By Raimer Kress

linear-algebra operator-theory hilbert-spaces

share|cite|improve this question

asked Mar 15 at 13:53

Inverse ProblemInverse Problem

1,009918

$endgroup$

migrated from mathoverflow.net Mar 15 at 18:21

This question came from our site for professional mathematicians.

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  what is $G$ here ?
  $endgroup$
  – Phil-W
  Mar 17 at 4:37
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @Phil-W,,,measurable set
  $endgroup$
  – Inverse Problem
  Mar 17 at 15:11
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  I'm guessing it's more than that, since you write C(G), you probably mean continuous functions on G right? So it has to be at least a topological space ?
  $endgroup$
  – Phil-W
  Mar 17 at 19:32
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @Phil-W...offcurse G is compact mesuarble and C is continuous fucntions on G
  $endgroup$
  – Inverse Problem
  Mar 18 at 7:11
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  It would help people to help you if you give all the hypothesis you are considering here, and also the notations, and not let them be forced to guess what you mean. For instance, do you suppose that the measure on $G$ is Radon ?
  $endgroup$
  – Phil-W
  Mar 19 at 20:06
  

  
  
  
  

add a comment | 

$begingroup$

Prove that $<C(G), C(G)>$ is dual system with bilinear form $$int_G phi(x)psi(x)dx $$ and $psi(x),psi(x)in C(G)$

so here i was trying bilinear form im not getting how to prove non-degenerate

definition of the non-degenerate bilinear form is in Linear Integral Equations
By Raimer Kress

linear-algebra operator-theory hilbert-spaces

share|cite|improve this question

asked Mar 15 at 13:53

Inverse ProblemInverse Problem

1,009918

$endgroup$

share|cite|improve this question

asked Mar 15 at 13:53

Inverse ProblemInverse Problem

1,009918

share|cite|improve this question

asked Mar 15 at 13:53

Inverse ProblemInverse Problem

1,009918

asked Mar 15 at 13:53

Inverse ProblemInverse Problem

1,009918

asked Mar 15 at 13:53

Inverse ProblemInverse Problem

1,009918