Harmonic functions on finitely sheeted unlimited covering surfaces

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Author(s)

Abstract

We denote by HP(R) and (HB(R), resp.) the class of positive (bounded, resp.) harmonic functions on a Riemann surface R. Consider an open Riemann surface W possessing a Green's function and a p-sheeted ( 1<p<∞) unlimited covering surface ˜{W} of W with projection map \varphi. We give a necessary and sufficient condition, in terms of Martin boundary, for HX(W)\circ\varphi=HX(˜{W})(X=P, B). We also give some examples illustrating the above result when W is the unit disc.

Journal

  • Journal of the Mathematical Society of Japan

    Journal of the Mathematical Society of Japan 55(2), 323-334, 2003-04-01

    The Mathematical Society of Japan

References:  15

Codes

  • NII Article ID (NAID)
    10011796503
  • NII NACSIS-CAT ID (NCID)
    AA0070177X
  • Text Lang
    ENG
  • Article Type
    ART
  • ISSN
    00255645
  • NDL Article ID
    6581669
  • NDL Source Classification
    ZM31(科学技術--数学)
  • NDL Call No.
    Z53-A209
  • Data Source
    CJP  NDL  J-STAGE 
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