Inequalities for hypercubic functionals. Generalized Chebyshev inequalities.

4 Jul 2021, 16:15


Armenak Gasparyan


By hypercubic functionals we mean expressions of type
$$ G_p{}^{(\sigma)}(\Phi,F) =\sum _{k \in B_2^p} (-1)^{(\sigma, k)}\Phi (k,F)\,\Phi (\overline{k},F) $$ where $\sigma \in B_2^p ={0,1}^p$,\, $\Phi :\,
B_2^p\times {\cal F} \to R(or\, C)$, and ${\cal F}\subseteq V^p$, $V$ --- some functional space. In very particular case $p=2$, this family of functionals contains
Binet-Cauchy, Chebyshev, Cauchy-Bunyakovsky-Schwarz, Newton,
Alexandrov and some other type functionals for which there hold well
known identities and inequalities.
By this talk, I think to familiarize colleagues with identities and
inequalities established for abovedefined hypercubic functionals.
Some applications also will be discussed.

Primary author

Armenak Gasparyan

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