On determination of best-possible constants in integral inequalities involving derivatives

Author:
Beny Neta

Journal:
Math. Comp. **35** (1980), 1191-1193

MSC:
Primary 26D15; Secondary 46E30, 65J99

DOI:
https://doi.org/10.1090/S0025-5718-1980-0583496-X

MathSciNet review:
583496

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Abstract: This paper is concerned with the numerical approximation of the best possible constants ${\gamma _{n,k}}$ in the inequality \[ {\left \| {{F^{(k)}}} \right \|^2} \leqslant \gamma _{n,k}^{ - 1}\;\left \{ {{{\left \| F \right \|}^2} + {{\left \| {{F^{(n)}}} \right \|}^2}} \right \},\] where \[ {\left \| F \right \|^2} = \int _0^\infty |F(x){|^2}\;dx.\] A list of all constants ${\gamma _{n,k}}$ for $n \leqslant 10$ is given.

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Article copyright:
© Copyright 1980
American Mathematical Society