Boundary properties of functions harmonic in a strip

  • V. I. Gorbaichuk
  • P. V. Zaderei


We study in the Lp-norm, 1≤p≤∞, the boundary properties of the solution to the Dirichlet problem for the stripA ={(x, y):−∞<x<∞, 0<y<η, η>0} and its dependence on the structural properties of the given boundary values (symmetric, antisymmetric). In particular, for the case of symmetric boundary values we obtain direct and inverse theorems on approximation in terms of the general modulus of continuity of second order.


Structural Property Dirichlet Problem General Modulus Boundary Property Symmetric Boundary 
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Literature cited

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    P. L. Butzer, W. Koble, and R. J. Nessel, “Approximation by functions harmonic in a strip,” Arch. Rational Mech. Anal.,44, No. 2, 329–336 (1972).Google Scholar
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    D. V. Widder, “Functions harmonic on a strip,” Proc. Am. Math. Soc.,12, 67–72 (1961).Google Scholar
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    D. V. Widder, “Fourier cosine transforms whose real parts are nonnegative in a strip,” Proc. Am. Math. Soc.,16, 1246–1252 (1965).Google Scholar
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    A. F. Timan, Theory of Approximation of Functions of a Real Variable [in Russian], Fizmatgiz, Moscow (1960).Google Scholar

Copyright information

© Plenum Publishing Corporation 1976

Authors and Affiliations

  • V. I. Gorbaichuk
    • 1
  • P. V. Zaderei
    • 1
  1. 1.Lutskii State Pedagogical InstituteUSSR

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