Geodesic
Entire functions that have the smallest deviation from zero with respect to the uniform norm with weight
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 41, Tome 416 (2013), pp. 98-107 Cet article a éte moissonné depuis la source Math-Net.Ru

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P. L. Chebyshev solved the problem of finding a polynomial of degree $n$ with leading coefficient one that has the smallest deviation from zero with respect to the maximum norm. A similar problem can be solved for some classes of entire functions. We find the entire function of exponential type $\sigma$ such that for any nonzero entire function $Q$ of type less than $\sigma$ and of class $A$ we have $$ \sup_\mathbb R\left|\frac{f_\sigma-Q}{\rho_m}\right|>\sup_\mathbb R\left|\frac{f_\sigma}{\rho_m}\right|. $$ 
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     author = {A. V. Gladkaya},
     title = {Entire functions that have the smallest deviation from zero with respect to the uniform norm with weight},
     journal = {Zapiski Nauchnykh Seminarov POMI},
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     year = {2013},
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     url = {http://geodesic.mathdoc.fr/item/ZNSL_2013_416_a4/}
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A. V. Gladkaya. Entire functions that have the smallest deviation from zero with respect to the uniform norm with weight. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 41, Tome 416 (2013), pp. 98-107. http://geodesic.mathdoc.fr/item/ZNSL_2013_416_a4/

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