Questions tagged [harmonic-functions]
For questions regarding harmonic functions.
211 questions
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Counting frequencies of occurrence of patterns within a sequence using harmonic analysis?
Assume that we are given a sequence $\mathbf x := X_1,\dots,X_n \in \mathbb N^n$ for some $n \in \mathbb N$. I am interested in calculating the frequency of occurrence of some fixed sequence $\mathbf ...
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Wavelets in the spaces of harmonic functions
I plan to do something with the theory of wavelets but in harmonic function theory. My question is about this interconnection between wavelets and harmonic functions. Can you recommend me some paper ...
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Subharmonic function on a twice punctured complex plane
is the twice punctured complex plane parabolic or hyperbolic? In this sense: does $\mathbb{C}-\{0,1\}$ admit a nonconstant, negative, subharmonic function?
Thanks,
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Existence of harmonic maps between loops
Given a Riemannian manifold $M$ and two smooth loops $\gamma_0, \gamma_1: S^1 \longrightarrow M$ in it, I am looking for maps $\phi: [0, T] \times S^1 \longrightarrow M$ which minimize the energy
$$E[\...
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What are the boundary asymptotics of harmonic symmetric transverse traceless rank-s tensors on $\mathbb{H}^n$ in the Poincare upper-half-space model? [closed]
This question is motivated by the results in this paper, http://calvino.polito.it/~camporesi/JMP94.pdf
In this paper some of its most important results about the asymptotics of symmetric traceless ...
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on an inequality of Brezis-Lieb
In their 1983 JFA paper Brezis and Lieb have shown, among many other things, a Poincaré-type inequality: in the case of a harmonic function $f$ on a bounded domain $\Omega$, their inequality ((3.14) ...
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Functions between Markov chains that preserve local harmonicity
Given two Markov chains with respective state-spaces $S$ and $T$, say that a function $\phi$ from $S$ to $T$ is holomorphic iff for all states $t \in T$, every real-valued function $f$ on $T$ that is ...
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refined Kato inequality
For any real-valued smooth function $u$, we have the Kato inequality
$|D|Du||^2\leq(det(Hess(u)))^2$,
which holds when $|Du|\neq0$.
If moreover $u$ is harmonic (in an open set in $\mathbb{R}^n$), ...
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Biharmonic function with a constant modulus
A bi-harmonic function $u:U\to C$, where $U$ is an open subset of the complex plane $C$ is a solution of the equation $\Delta^2u=0$. Can a nonconstant bi-harmonic mapping have a constant modulus in an ...
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Biharmonic function
Is a family of bounded bi-harmonic functions defined in the unit disk an equicontinuous family of functions on compacts? A bi-harmonic function $u$ is a solution of the equation $\Delta^2 u =0$.
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Harmonic functions on the plane
I have a question regarding harmonic maps from all of ${\Bbb R}^2$ into a domain in ${\Bbb R}^2$. Before stating my question in full generality, let me ask a special case of the question first. Is it ...
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