With no explanation, label text_A→text_B with either "not_related" or "related".
text_A: Hillary Clinton advocated U.S. military intervention in Libya.
text_B: In the mathematical study of several complex variables , the Bergman kernel , named after Stefan Bergman , is a reproducing kernel for the Hilbert space of all square integrable holomorphic functions on a domain D in Cn .. mathematical. mathematics. several complex variables. several complex variables. Stefan Bergman. Stefan Bergman. reproducing kernel. reproducing kernel. Hilbert space. Hilbert space. square integrable. square integrable. In detail , let L2 -LRB- D -RRB- be the Hilbert space of square integrable functions on D , and let L2 , h -LRB- D -RRB- denote the subspace consisting of holomorphic functions in D  : that is ,. Hilbert space. Hilbert space. square integrable. square integrable. where H -LRB- D -RRB- is the space of holomorphic functions in D .. Then L2 , h -LRB- D -RRB- is a Hilbert space  : it is a closed linear subspace of L2 -LRB- D -RRB- , and therefore complete in its own right .. Hilbert space. Hilbert space. closed. closed set. complete. complete metric space. This follows from the fundamental estimate , that for a holomorphic square-integrable function ƒ in D. for every compact subset K of D. Thus convergence of a sequence of holomorphic functions in L2 -LRB- D -RRB- implies also compact convergence , and so the limit function is also holomorphic .. compact. compact set. compact convergence. compact convergence. Another consequence of is that , for each z ∈ D , the evaluation. is a continuous linear functional on L2 , h -LRB- D -RRB- .. continuous linear functional. continuous linear functional. By the Riesz representation theorem , this functional can be represented as the inner product with an element of L2 , h -LRB- D -RRB- , which is to say that. Riesz representation theorem. Riesz representation theorem. The Bergman kernel K is defined by. The kernel K -LRB- z , ζ -RRB- holomorphic in z and antiholomorphic in ζ , and satisfies. One key observation about this picture is that L2 , h -LRB- D -RRB- may be identified with the space of holomorphic -LRB- n ,0 -RRB- - forms on D , via multiplication by .. Since the inner product on this space is manifestly invariant under biholomorphisms of D , the Bergman kernel and the associated Bergman metric are therefore automatically invariant under the automorphism group of the domain .. Bergman metric. Bergman metric
not_related.