TOPICS
Search

Faltung


The term faltung is variously used to mean convolution and a function of bilinear forms.

Let A and B be bilinear forms

A=A(x,y)=sumsuma_(ij)x_iy_i
(1)
B=B(x,y)=sumsumb_(ij)x_iy_i
(2)

and suppose that A and B are bounded in [p,p^'] with bounds M and N. Then

 F=F(A,B)=sumsumf_(ij)x_iy_j,
(3)

where the series

 f_(ij)=sum_(k)a_(ik)b_(kj)
(4)

is absolutely convergent, is called the faltung of A and B. F is bounded in [p,p^'], and its bound does not exceed MN.


See also

Convolution

Explore with Wolfram|Alpha

References

Hardy, G. H.; Littlewood, J. E.; and Pólya, G. Inequalities, 2nd ed. Cambridge, England: Cambridge University Press, pp. 210-211, 1988.

Referenced on Wolfram|Alpha

Faltung

Cite this as:

Weisstein, Eric W. "Faltung." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Faltung.html

Subject classifications