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Multi-Dimensional Landau Extremum Problems


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1 The National University of Athens, Pedagogical Dept., E.E. 4, Agamemnonos Str. Aghia Paraskevi, Attikis-15342, Greece
     

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Edmund Landau [5] initiated the following extremum problem: The sharp inequality between the supremum-norms of derivatives of twice differentiable functions f such that
f'‖2≤4‖f‖ ‖f"‖                                                 (+)
holds with norm referring to the space C[0,∞]. In this work we extend Landau’s results and establish new multi-dimensional inequalities of Landau type for semigroups and cosine functions.
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  • Multi-Dimensional Landau Extremum Problems

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Authors

J. M. Rassias
The National University of Athens, Pedagogical Dept., E.E. 4, Agamemnonos Str. Aghia Paraskevi, Attikis-15342, Greece

Abstract


Edmund Landau [5] initiated the following extremum problem: The sharp inequality between the supremum-norms of derivatives of twice differentiable functions f such that
f'‖2≤4‖f‖ ‖f"‖                                                 (+)
holds with norm referring to the space C[0,∞]. In this work we extend Landau’s results and establish new multi-dimensional inequalities of Landau type for semigroups and cosine functions.