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The normality of the logarithmic derivative

The normality of the logarithmic derivative
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LOGARITHMIC VERSION OF INTERPOLATION INEQUALITIES FOR DERIVATIVES

Journal of the London Mathematical Society, 2004
The classical Gagliardo-Nirenberg inequality \[ \| \nabla^{(k)} u \| _q \leq C \, \| u \| ^{1-k/m}_r \| \nabla^{(m)} u \| ^{k/m}_p \] in \(R^n ...
Kałamajska, Agnieszka, Pietruska-Pałuba, Katarzyna   +1 more
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Deriving Phase from Logarithmic Gain Derivatives

Circuits, Systems & Signal Processing, 2002
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Rusu, Corneliu, Gavrea, Ioan, Kuosmanen, Pauli   +2 more
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Newq-derivative andq-logarithm

International Journal of Theoretical Physics, 1994
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Chung, Ki-Soo, Chung, Won-Sang, Nam, Sang-Tack, Kang, Hye-Jung   +3 more
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Logarithmic derivatives of theta functions

Israel Journal of Mathematics, 2005
The authors give two new proofs of the identity \[ \sum_{n=0}^\infty \delta(3n+1)x^n= \prod_{n=1}^\infty \frac{(1-x^{3n})^3} {(1-x^n)} \] where \(\delta(n)= d_1(n)- d_2(n)\) is the number of divisors of \(n\) congruent to \(i\bmod 3\). The main tool of the proofs is the theory of theta functions with characteristics: \[ \theta\biggl[ {{\varepsilon ...
Farkas, Hershel M., Godin, Yves
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On the Growth of the Logarithmic Derivative

Computational Methods and Function Theory, 2001
Let \(f\) be a meromorphic function on \(\mathbb{C}\) with \(f(0)=1\). \textit{A. Gol'dberg} and \textit{V. Grinshtein} [Math. Notes 19, 320-323 (1976; Zbl 0338.30020)] sharpened the lemma of logarithmic derivative in Nevanlinna theory as follows: \[ m\left(r,\frac{f'}{f}\right)\leq \log^+\frac{\rho T(\rho,f)}{r(\rho-r)}+ c, \] where \(\rho>r\), \(c ...
Benbourenane, Djamel, Korhonen, Risto
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Linear Differential Equations and Logarithmic Derivative Estimates

Proceedings of the London Mathematical Society, 2003
The linear differential equation \[ f^{(k)}+A_{k-1}(z)f^{(k-1)}+\ldots+A_0(z)f=0 \tag{1} \] is considered, where \(A_n(z)\), \(n=0,1,\dots,k-1\), are analytic functions in the unit disk \(\Delta= \{z: | z|
Chyzhykov, Igor, Gundersen, Gary G., Heittokangas, Janne   +2 more
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Extremal Properties of Logarithmic Derivatives of Polynomials

Journal of Mathematical Sciences, 2020
In this paper, some important problems connected with extremal and approximation properties of simple partial rational functions have been studied. It has been proved that for any \(a>1\) the poles of a partial function \(\rho_{n}\) whose sup norm does not exceed \(\ln(1+a^{-1})\) on \([-1,1]\) lie in the exterior of the ellipse with foci \(\pm 1\) and
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The Derivative of the Logarithm

The American Mathematical Monthly, 1916
(1916). The Derivative of the Logarithm. The American Mathematical Monthly: Vol. 23, No. 6, pp. 204-206.
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