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Multi-Dimensional Landau Extremum Problems
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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.
‖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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