Results 281 to 290 of about 93,097 (321)
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Modulus of continuity of harmonic functions
Journal d'Analyse Mathématique, 1988Suppose 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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Modulus of Continuity for Stochastic Flows
1993In this article we determine the modulus of continuity for a class of stochastic flows. We also give an application to anticipating stochastic differential equations of the Stratonovich type.
Paolo Baldi, Marta Sanz-Solé
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Majorization of the Modulus of Continuity of Analytic Functions
Computational Methods and Function Theory, 2007Let \(G\) be an open set in the complex plane, \(f\) analytic in \(G\) and continuous in \(\overline G\). Let \(\mu\) is a majorant in the sense that \(\mu(t)\) is a nonnegative, nondecreasing function defined for \(t\geq 0\) with \(\mu(2t)\leq 2\mu(t)\) for all \(t\geq 0\) and \[ |f(z_1)- f(z_2)|\leq \mu(|z_1- z_2|)\tag{1} \] for \(z_1\) and \(z_2 ...
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Modulus of continuity of the Weierstrass function
Mathematical Notes of the Academy of Sciences of the USSR, 1984Translation from Mat. Zametki 36, No.1, 35-38 (Russian) (1984; Zbl 0543.42007).
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On the integral modulus of continuity of fourier series
Journal d'Analyse Mathématique, 1972Ram Babu. On the integral modulus of continuity of Fourier series. In: Bulletin de la Classe des sciences, tome 58, 1972. pp. 337-343.
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Modulus of Continuity for Peierls’s Barrier
1987For an exact area preserving monotone twist diffeomorphism with a uniform lower bound β for the amount of twisting, we will show that Peierls’s barrier satisfies $$ \left| {{P_{p/q}}\left( \xi \right) - {P_\omega }\left( \xi \right)} \right| \leqslant C\left( {{q^{ - 1}} + \left| {\omega q - p} \right|} \right) $$ , where C = (1200)cotβ.
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Averaged modulus of continuity and bracket compactness
Mathematical Notes, 2010zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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A Continuous Modulus of Continuity
The American Mathematical Monthly, 1975Stephen B. Seidman, J. A. Childress
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Mathematics of the USSR-Sbornik, 1985
Let G be a set, S its subset, \(\omega:[0,+\infty)\to [0,+\infty)\) an increasing function with \(\omega(0)=(0)\) and \(\omega(\delta_ 1+\delta_ 2)\leq \omega(\delta_ 1)+\omega(\delta_ 2)\) for all \(\delta_ 1,\delta_ 2>0\). For any \(f:G\to {\mathbb{C}}\) put \(\omega_{S,f}(\delta)=^{def}\sup \{| f(\zeta)-f(z)|:z,\zeta \in S,\quad | \zeta -z| \leq ...
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Let G be a set, S its subset, \(\omega:[0,+\infty)\to [0,+\infty)\) an increasing function with \(\omega(0)=(0)\) and \(\omega(\delta_ 1+\delta_ 2)\leq \omega(\delta_ 1)+\omega(\delta_ 2)\) for all \(\delta_ 1,\delta_ 2>0\). For any \(f:G\to {\mathbb{C}}\) put \(\omega_{S,f}(\delta)=^{def}\sup \{| f(\zeta)-f(z)|:z,\zeta \in S,\quad | \zeta -z| \leq ...
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The generalized modulus of continuity and wavelets
1994Over 20 years ago I introduced a flexible instrument to measure regularity of functions on Euclidean space which I called the generalized modulus of continuity or, m-modulus, with m denoting an arbitrary bounded complex measure on n-space whose Fourier transform vanishes at the origin.
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