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Quadrature and Harmonic Approximation of Subharmonic Functions in Strips
Author(s) -
Armitage D. H.,
Goldstein M.
Publication year - 1992
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/s2-46.1.171
Subject(s) - subharmonic , strips , quadrature (astronomy) , harmonic function , mathematics , norm (philosophy) , mathematical analysis , subharmonic function , harmonic , physics , nonlinear system , algorithm , acoustics , optics , quantum mechanics , political science , law
Open sets D in R N (N ⩾ 2) with the property that D ¯ is a closed strip (that is, a set of the form [ a, b ]× R N−1 ) are characterized by a quadrature formula for harmonic functions. This characterization is used to prove a theorem on approximation in the L 1 norm of subharmonic functions in strips by harmonic functions.