Growth of harmonic functions on biregular trees

AbstractIt is shown to be consistent with set theory that every set of reals of size ℵ1 is null yet there are ℵ1 planes in Euclidean 3-space whose union is not null. Similar results will be obtained for other geometric objects. The proof relies on results from harmonic analysis about the boundedness of certain harmonic functions and a measure theoretic pigeonhole principle.

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Analytic Capacity and Differeatiability Properties of Finely Harmonic Functions: Summary

Real Analysis Exchange ◽

10.2307/44151574 ◽

1982 ◽

Vol 8 (1) ◽

pp. 24

Author(s):

Davie ◽

Øksendal

Keyword(s):

Harmonic Functions ◽

Analytic Capacity

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On the existence of various bounded harmonic functions with given periods, II

Nagoya Mathematical Journal ◽

10.1017/s0027763000016317 ◽

1975 ◽

Vol 56 ◽

pp. 1-5

Author(s):

Masaru Hara

Keyword(s):

Riemann Surface ◽

Harmonic Function ◽

Harmonic Functions ◽

Dirichlet Integral ◽

Period Function ◽

Boundedness Property ◽

One Dimensional ◽

Bounded Harmonic Functions

Given a harmonic function u on a Riemann surface R, we define a period functionfor every one-dimensional cycle γ of the Riemann surface R. Γx(R) denote the totality of period functions Γu such that harmonic functions u satisfy a boundedness property X. As for X, we let B stand for boundedness, and D for the finiteness of the Dirichlet integral.

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Least squares prediction of gravity anomalies, geoidal undulations, and deflections of the vertical with multiquadric harmonic functions

Geophysical Research Letters ◽

10.1029/gl002i010p00423 ◽

1975 ◽

Vol 2 (10) ◽

pp. 423-426 ◽

Cited By ~ 39

Author(s):

R. L. Hardy ◽

W. M. Göpfert

Keyword(s):

Least Squares ◽

Harmonic Functions ◽

Gravity Anomalies ◽

Deflections Of The Vertical

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Linking the FK5 to the ICRF

Highlights of Astronomy ◽

10.1017/s1539299600020840 ◽

1998 ◽

Vol 11 (1) ◽

pp. 313-316

Author(s):

F. Mignard ◽

M. Froeschile

Keyword(s):

Reference Frame ◽

Proper Motion ◽

Harmonic Functions ◽

Optical Reference ◽

Precessional Motion ◽

Precession Constant

Abstract The Hipparcos optical reference frame is compared to the basic FK5 in order to determine the orientation at T0 = 1991.25 and the global spin between the two frames. The components of the spin are significant and suggest a correction the IAU76 value of the precession constant and to a possible non-precessional motion of the equinox of the FK5. The regional errors are analysed with harmonic functions and found to be as large as 150 mas in position and 3 mas/yr in proper motion.

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