Harmonic Function in Chromatic Music: A Renewed Dualist Theory and an Account of Its Precedents Daniel Harrison

1996 ◽  
Vol 18 (1) ◽  
pp. 124-133 ◽  
Author(s):  
Richard A. Kaplan
Keyword(s):  
Harmonic Function ◽  
Chromatic Music

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

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.

Kelvin-Möbius-Invariant Harmonic Function Spaces on the Real Unit Ball

2021 ◽  
pp. 125298
Author(s):  
H. Turgay Kaptanoğlu ◽  
A. Ersin Üreyen
Keyword(s):  
Harmonic Function ◽  
Unit Ball ◽  
Function Spaces ◽  
The Real

scholarly journals A note on n-harmonic majorants

1986 ◽  
Vol 34 (3) ◽  
pp. 461-472
Author(s):  
Hong Oh Kim ◽  
Chang Ock Lee
Keyword(s):  
Harmonic Function ◽  
Complex Plane ◽  
Unit Disc ◽  
Dirichlet Integral ◽  
Harmonic Majorant ◽  
Harmonic Majorants

Suppose D (υ) is the Dirichlet integral of a function υ defined on the unit disc U in the complex plane. It is well known that if υ is a harmonic function in U with D (υ) < ∞, then for each p, 0 < p < ∞, |υ|p has a harmonic majorant in U.We define the “iterated” Dirichlet integral Dn (υ) for a function υ on the polydisc Un of Cn and prove the polydisc version of the well known fact above:If υ is an n-harmonic function in Un with Dn (υ) < ∞, then for each p, 0 < p < ∞, |υ|p has an n-harmonic majorant in Un.

scholarly journals Gradient estimates for weighted harmonic function with Dirichlet boundary condition

2021 ◽  
Vol 213 ◽  
pp. 112498
Author(s):  
Nguyen Thac Dung ◽  
Jia-Yong Wu
Keyword(s):  
Boundary Condition ◽  
Harmonic Function ◽  
Dirichlet Boundary Condition ◽  
Dirichlet Boundary ◽  
Gradient Estimates

scholarly journals Harmonic Morphisms Projecting Harmonic Functions to Harmonic Functions

2012 ◽  
Vol 2012 ◽  
pp. 1-8
Author(s):  
M. T. Mustafa
Keyword(s):  
Harmonic Function ◽  
Riemannian Manifolds ◽  
Harmonic Functions ◽  
Horizontal Component ◽  
Harmonic Morphisms

For Riemannian manifoldsMandN, admitting a submersionϕwith compact fibres, we introduce the projection of a function via its decomposition into horizontal and vertical components. By comparing the Laplacians onMandN, we determine conditions under which a harmonic function onU=ϕ−1(V)⊂Mprojects down, via its horizontal component, to a harmonic function onV⊂N.

On the fatou theorem for p-harmonic function

1988 ◽  
Vol 13 (6) ◽  
pp. 651-668 ◽  
Author(s):  
Juan J. Manfredi ◽  
Allen Weitsman
Keyword(s):  
Harmonic Function ◽  
Fatou Theorem
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