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Harmonic and Subharmonic RF Injection Locking of THz Metasurface Quantum-Cascade VECSEL. [PDF]

ACS Photonics
Wu Y, Schreiber MA, Kim AD, Addamane SJ, Jirauschek C, Williams BS.   +5 more
europepmc   +1 more source

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Conditions for separately subharmonic functions to be subharmonic

Potential Analysis, 1993
Let \(\Omega\) be an open set in \(\mathbb{R}^ m \times \mathbb{R}^ n\). A function \(u\) is separately subharmonic on \(\Omega\) if \(u(x,\cdot)\) is subharmonic on the \(x\)-section of \(\Omega\), and \(u(\cdot,y)\) on the \(y\)-section, for all \((x,y) \in\Omega\).
D H Armitage
exaly   +2 more sources

Approximation to subharmonic functions by subharmonic polynomials

Mathematical Notes, 1985
Let D be a domain in \({\mathcal R}^ m\) (m\(\geq 2)\) with connected boundary and let E be a compact subset of D. It is shown that if u is real-valued, continuous and subharmonic in D, then u can be uniformly approximated in E by subharmonic polynomials. This result with ''harmonic'' in place of ''subharmonic'' is a classical theorem of J. L.
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Paths for Subharmonic Functions

Proceedings of the London Mathematical Society, 1984
The paths are investigated for non-negative subharmonic functions defined on the domains in \(R^ m\), \(m=2\), 3. Let u be a subharmonic function on the unit ball B(0,1) of \(R^ n\) and 0\(\leq u\leq 1\). Then for given \(\epsilon>0\) there exists \(r(\epsilon)>0\) with the following property: if \(| x-y|\epsilon\), \(u(y)>\epsilon\), \(| x|
Davis, Burgess, Lewis, John L.
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APPROXIMATION OF SUBHARMONIC FUNCTIONS

Mathematics of the USSR-Sbornik, 1985
If the function f(z) is holomorphic in \(\Omega \subset R_ 2\), the function ln \(| f(z)|\) is subharmonic in \(\Omega\). In the paper the possibilities of approximations of subharmonic functions defined on an arbitrary domain \(\Omega \subset R_ 2\) are studied. For the case \(\Omega =R_ 2\) the problem is also solved. The approximation is realized by
openaire   +4 more sources

AN ESTIMATE FOR THE SUBHARMONIC DIFFERENCE OF SUBHARMONIC FUNCTIONS. I

Mathematics of the USSR-Sbornik, 1977
Let , , and be subharmonic functions in the half-plane , and suppose that and are majorized by a positive function of the form , where and .An inequality for the subharmonic difference is obtained in terms of the function , , , which then gives an estimate for the difference from above.
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Conditions for subharmonicity and subharmonic extensions of functions

Sbornik: Mathematics, 2017
This paper establishes a general result about removable sets for subharmonic functions \(u\) based on the behaviour of the mean value \(M_{r}u(x)\) of \(u\) over the ball \(B(x,r)\) as \(r\rightarrow 0+\). Several applications are presented, of which a sample is now given.
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Subharmonic Functions in the Unit Ball

Positivity, 2005
Let $u$ be a subharmonic function on the unit ball $B_{N}$ in $\Bbb{R}^N$ $(N\geq2)$, and let $µ$ be its associated Riesz measure. This paper establishes growth properties of $µ(s)\coloneq µ(\{\vert x\vert\leq s\})$ when growth restrictions are imposed on $u$. For example, let $g$ denote the Green function for $B_{N}$ with pole at $0$, and suppose that
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Length of Paths for Subharmonic Functions

Journal of the London Mathematical Society, 1985
Let D be a simply connected domain in the complex plane and let a be a point in D. Let u be a subharmonic function on D with values in [0,1] such that \(u(a)>0\). The author shows that there exists a path \(\gamma\) joining a with a point b on the boundary of D such that \(\gamma\) \(\setminus \{b\}\subset D\) and \(4u>u(a)\) on \(\gamma\) \(\setminus \
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Subharmonic and h-Subharmonic Functions

2016
Miroljub Jevtić, Dragan Vukotić, Miloš Arsenović   +2 more
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