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Duke Mathematical Journal, 1943 Some of the next articles are maybe not open access.
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Increasing functions, harmonic bloch and harmonic normal functions
Complex Variables, Theory and Application: An International Journal, 1999In this note, characterization for harmonic Bloch functions and harmonic normal functions are given by means of increasing functions.
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1992
In Chapter 2 we proved that a bounded harmonic function on R n is constant. We now improve that result.
Wade Ramey +2 more
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In Chapter 2 we proved that a bounded harmonic function on R n is constant. We now improve that result.
Wade Ramey +2 more
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1992
Liouville’s Theorem in complex analysis states that a bounded holo-morphic function on C is constant. A similar result holds for harmonic functions on R n . The simple proof given below is taken from Edward Nelson’s paper [7], which is one of the rare mathematics papers not containing a single mathematical symbol.
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Liouville’s Theorem in complex analysis states that a bounded holo-morphic function on C is constant. A similar result holds for harmonic functions on R n . The simple proof given below is taken from Edward Nelson’s paper [7], which is one of the rare mathematics papers not containing a single mathematical symbol.
Wade Ramey +2 more
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Quaestiones Mathematicae, 2002
Abstract unavailable at this time...Mathematics Subject Classification (2000): Primary 31B05; Secondary 47A16 Quaestiones Mathematicae 25 (2002), 527 ...
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Abstract unavailable at this time...Mathematics Subject Classification (2000): Primary 31B05; Secondary 47A16 Quaestiones Mathematicae 25 (2002), 527 ...
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Partition Function for the Harmonic Oscillator
1992We start by making the following changes from Minkowski real time t = x0 to Euclidean “time” τ = tE:
Walter Dittrich, Martin Reuter
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Sets of Harmonicity for Finely Harmonic Functions
Potential Analysis, 2004Given an open set U in Rn (n≥3) and a dense open subset V of U, it is shown that there is a finely harmonic function u on U such that V is the largest open subset of U on which u is harmonic. This result, which establishes the sharpness of a theorem of Fuglede, is obtained following a consideration of fine cluster sets of arbitrary functions.
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A note on harmonic functions and harmonic conjugates
International Journal of Mathematical Education in Science and Technology, 1977An. algebraic method, which eliminates the need for integration, for determining the general analytic function, given its real or imaginary part (or suitable combination of real and imaginary part) is presented. Good examples illustrating the techniques are then given.
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Sequences of Harmonic Functions
1929We have already found need of the fact that certain infinite series of harmonic functions converge to limiting functions which are harmonic. We are now in a position to study questions of this sort more system- atically.
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