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K- andL-kernels on an arbitrary Riemann surface

1966
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Pacific Journal of Mathematics
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The Z-kernel which was first considered by Schiffer for plane regions is extended to arbitrary open Riemann surfaces for a number of significant subspaces of the space of square integrable harmonic differentials Γ h . The Z-kernel for each of the subspaces considered is expressed in terms of the principal functions. Thus if W is an open Riemann surface and p and q the L x principal functions of W with singularities Re 1/z and Im 1/z respectively, then the following result is proved. THEOREM.

doi:10.2140/pjm.1966.19.449
fatcat:qtyqu77yqjfsllp4zqlf5vvu4q