Results 141 to 150 of about 1,361 (182)
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APPROXIMATION OF SUBHARMONIC FUNCTIONS
Mathematics of the USSR-Sbornik, 1985If 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
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AN ESTIMATE FOR THE SUBHARMONIC DIFFERENCE OF SUBHARMONIC FUNCTIONS. I
Mathematics of the USSR-Sbornik, 1977Let , , 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 separately subharmonic functions to be subharmonic
Potential Analysis, 1993Let \(\Omega\) 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 \((x,y) \in\Omega\).
Armitage, D. H., Gardiner, Stephen J.
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Approximation to subharmonic functions by subharmonic polynomials
Mathematical Notes of the Academy of Sciences of the USSR, 1985Let 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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Conditions for subharmonicity and subharmonic extensions of functions
Sbornik: Mathematics, 2017This 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, 2005Let $u$ 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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On a Class of Subharmonic Functions
Mathematische Nachrichten, 1973Jain, P. K., Gupta, P. N., Gupta, V. P.
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The logarithm of the modulus of a holomorphic function as a minorant for a subharmonic function
Mathematical Notes, 2016Bulat Khabibullin, Khabibullin B N
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