Schwartz kernel theorem

<p>In <a href="/facts/Mathematics/pxTouaz4">mathematics</a>, the Schwartz kernel theorem is a foundational result in the theory of <a href="/facts/Generalized_function/fCM4VsyT">generalized functions</a>, published by <a href="/facts/Laurent_Schwartz/Kxelk3ju">Laurent Schwartz</a> in 1952. It states, in broad terms, that the generalized functions introduced by Schwartz (<a href="/facts/Schwartz_distribution/yfaJ4mUp">Schwartz distributions</a>) have a two-variable theory that includes all reasonable <a href="/facts/Bilinear_form/gyvzn9ym">bilinear forms</a> on the space 
  
    
      
        
          
            D
          
        
      
    
    {\displaystyle {\mathcal {D}}}
  
 of <a href="/facts/Test_functions/yfaJ4mUp">test functions</a>. The space 
  
    
      
        
          
            D
          
        
      
    
    {\displaystyle {\mathcal {D}}}
  
 itself consists of <a href="/facts/Smooth_function/mffL4ch2">smooth functions</a> of <a href="/facts/Compact_support/BTuMGbsb">compact support</a>.
</p>

Schwartz kernel theorem open-in-new

Schwartz kernel theorem