Indefinite Hardy spaces on finite bordered Riemann surfaces (Q1976337)

Indefinite inner products obtained by picking up different signs when integrating over different components were considered. Necessary and sufficient conditions were found for such an indefinite inner product to be nondegenerate. It was shown that when this condition is satisfied a Krein space is received. The elements of the space are sections of a vector bundle rather than functions. Appropriate extension of this bundle to the double of the finite bordered Riemann surface was constructed.