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On Maximum Modulus of Polynomials with Restricted Zeros
Bulletin of the Iranian Mathematical Society, 2021zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Chanam, Barchand +3 more
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On the Maximum Modulus and the Mean Modulus of an Entire Function
Canadian Mathematical Bulletin, 1969Let be an entire function, but not a polynomial.
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2011
In this lecture, we shall prove that a function analytic in a bounded domain and continuous up to and including its boundary attains its maximum modulus on the boundary. This result has direct applications to harmonic functions.
Ravi P. Agarwal +2 more
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In this lecture, we shall prove that a function analytic in a bounded domain and continuous up to and including its boundary attains its maximum modulus on the boundary. This result has direct applications to harmonic functions.
Ravi P. Agarwal +2 more
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Derivatives of the maximum modulus of a starlike function
Analysis Mathematica, 1981Let \(f\) be analytic in the unit disk \(D\) and \(M(r,f)=\max\{| f(z)|\mid| z|= r\}\) for \(r\in (0,1)\). In this paper the author describes the very delicate construction of a function \(f\) and a sequence \((r_ n)_{n\in\mathbb{N}}= (r_ n(f))_{n\in\mathbb{N}}\) with the following properties: 1) \(f(0)= f'(0)- 1=0\), \(f\) is starlike in \(D\), 2 ...
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Maximum Modulus Sets and Segre Convexity
Mathematische Nachrichten, 2001In this paper the authors investigate the relation between the Segre convexity of the boundary \( b\Omega\) of a domain \( \Omega\) in \(\mathbb C^{n}\) and the positivity of the (local) canonical defining function for \(( b \Omega, E, \mathcal F)\), where \(E\) is an \(n\)-dimensional, totally real submanifold of \( b\Omega\) foliated by interpolation
Cœuré, Gérard, Honvault, Pascal
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1973
This chapter continues the study of a property of analytic functions first seen in Theorem IV. 3.11. In the first section this theorem is presented again with a second proof, and other versions of it are also given. The remainder of the chapter is devoted to various extensions and applications of this maximum principle.
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This chapter continues the study of a property of analytic functions first seen in Theorem IV. 3.11. In the first section this theorem is presented again with a second proof, and other versions of it are also given. The remainder of the chapter is devoted to various extensions and applications of this maximum principle.
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ON THE MAXIMUM MODULUS PATHS OF A CERTAIN CUBIC
The Quarterly Journal of Mathematics, 1986Let \(\beta >0\), \(\alpha \beta >1+2\beta\), and consider a polynomial \(z^ 3+\alpha z^ 2-z+\beta\). It is shown that its maximum modulus M(r) is taken on some path from 0 to -1 and then from \(+1\) to \(\infty\), i.e. there is a jump for \(r=1\). In the last formula 2r should be 4r.
Jassim, S. A., London, R. R.
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