**Are you an EPFL student looking for a semester project?**

Work with us on data science and visualisation projects, and deploy your project as an app on top of GraphSearch.

Concept# Schur test

Summary

In mathematical analysis, the Schur test, named after German mathematician Issai Schur, is a bound on the L^2\to L^2 operator norm of an integral operator in terms of its Schwartz kernel (see Schwartz kernel theorem).
Here is one version. Let X,,Y be two measurable spaces (such as \mathbb{R}^n). Let ,T be an integral operator with the non-negative Schwartz kernel ,K(x,y), x\in X, y\in Y:
:T f(x)=\int_Y K(x,y)f(y),dy.
If there exist real functions ,p(x)>0 and ,q(y)>0 and numbers ,\alpha,\beta>0 such that
: (1)\qquad \int_Y K(x,y)q(y),dy\le\alpha p(x)
for almost all ,x and
: (2)\qquad \int_X p(x)K(x,y),dx\le\beta q(y)
for almost all ,y, then ,T extends to a continuous operator T:L^2\to L^2 with the operator norm
: \Vert T\Vert_{L^2\to L^2} \

Official source

This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.

Related publications

Loading

Related people

Loading

Related units

Loading

Related concepts

No results

Related courses

Loading

Related lectures

Loading

Related people

No results

Related publications

No results

Related lectures

Related units

Related courses

No results

No results

No results