TOPICS
Search

Reznick's Identity

For P and Q polynomials in n variables,

|P·Q|_2^2=sum_(i_1,...,i_n>=0)(|P^((i_1,...,i_n))(D_1,...,D_n)Q(x_1,...,x_n)|_2^2)/(i_1!...i_n!),

where D_i=partial/partialx_i, |X|_2 is the Bombieri norm, and

P^((i_1,...,i_n))=D_1^(i_1)...D_n^(i_n)P.

Bombieri's inequality follows from this identity.

See also

Beauzamy and Dégot's Identity

Explore with Wolfram|Alpha

References

Reznick, B. "An Inequality for Products of Polynomials." Proc. Amer. Math. Soc. 117, 1063-1073, 1993.

Referenced on Wolfram|Alpha

Reznick's Identity

Cite this as:

Weisstein, Eric W. "Reznick's Identity." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/ReznicksIdentity.html

Subject classifications