## Generalized Analytic Functions on Riemann Surfaces |

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### Contents

The Dolbeault and RiemannRoch theorems | 1 |

Linear integral equations connected with | 29 |

The Riemann boundary problem | 66 |

Copyright | |

5 other sections not shown

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### Common terms and phrases

2iri Abelian covariant Abelian differentials Abelian integral analytic covariants analytic functions arbitrary argument principle basis belongs bundle Ca(G called Carleman-Bers-Vekua Cauchy kernel Cauchy-Riemann equation coboundary cochain cocycle coefficients cohomology groups coincides compact completely continuous Consider coordinate corresponding cycles defined denoted determined differential form divisor domain G dz(p dz(s equal to zero equation 3u equation S*v exact sequence fixed point follows formula func function in G genus hence holomorphic functions I.N. Vekua integral equation linear combination Lp(G mapping Math matrix Mikhailov multi-valued function norm obtain the relation operator Poincare lemma q-cochains regular solution representable respectively Riemann problem Riemann-Roch theorem Rodin S.P. Novikov satisfying the conditions sections Serre duality sheaf of germs sheaves single-valued solutions singularities solution of equation solvable space S(d,a,M theory tion triangles type i,j uQ(s V.E. Zakharov valid Yu.L zeros and poles