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ON MAXIMUM MODULUS OF ANALYTIC FUNCTIONS

ON MAXIMUM MODULUS OF ANALYTIC FUNCTIONS
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Modulus of Continuity of Piecewise Analytic Functions

Mathematical Notes, 2003
Conditions under which the modulus of continuity \(\omega(f; \delta)\) of a piece-wise real-analytic function \(f : [a, b] \rightarrow {\mathbb R}\) becomes analytic at zero are found. The results obtained are of the following type. Theorem 1. Let \(f\) be piece-wise real-analytic on \([a, b]\). If \[ \sup_{x\in D_{N}} d(x) < \sup_{x\in M\setminus D_{N}
Dovgosheĭ, A. A., Potemkina, L. L.
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Local Maximum Modulus Property for Polyanalytic Functions

Complex Analysis and Operator Theory, 2015
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Daghighi, Abtin, Krantz, Steven G.
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Minimum modulus of small entire functions

Complex Variables, Theory and Application: An International Journal, 1996
Minimum modulus theorems are important in applications where one has to divide by a given entire function. In this paper, we shall use a very simple and fundamental method to strengthen a theorem of A. Edrei on the minimum modulus of entire functions of order less than one.
Xinhou Hua, Zhengshan Lin
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Comments on the electric modulus function

Journal of Non-Crystalline Solids, 2005
Arguments in favor of the electric modulus formalism are reviewed, and several misunderstandings and misrepresentations are corrected. It is argued that different representations of the same experimental data provide additional, rather then subtractive, insights into the difficult problem of understanding ionic conductivity in melts, glasses and ...
I.M. Hodge, K.L. Ngai, C.T. Moynihan
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Shear modulus of Laughlin-type wave functions

Physical Review B, 1986
Using the excited states of Girvin, Macdonald, and Platzman and the fluid ground state proposed by Laughlin, the shear modulus is calculated as a strain autocorrelation function and is found to be finite (0.0056${e}^{2}$/${l}^{3}$).
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The Modulus as a Set Function

2020
Let E and F be compact disjoint non-empty sets in \(\overline {\mathbb {R}}^n\) and \(\mathsf {M}( \Delta _{EF})=\mathsf {M}\bigl (\Delta (E,F)\bigr )\).
Parisa Hariri, Riku Klén, Matti Vuorinen   +2 more
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Modulus of continuity of harmonic functions

Journal d'Analyse Mathématique, 1988
Suppose that u(z) is a harmonic function in a plane domain G and that the modulus of continuity of u(z) is majorised by a nondecreasing function \(\mu\) (t), \(\mu\) (2t)\(\leq 2\mu (t)\), on the boundary \(\partial G\). What kind of upper bound can be obtained for \(| u(z_ 1)-u(z_ 2)|\) when \(z_ 1,z_ 2\in \bar G?\) Making use of various estimates of ...
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