[tex]\varphi(x)=f(x)+\int^{b}_{a}K(x,y)\varphi(y)dt[/tex](adsbygoogle = window.adsbygoogle || []).push({});

[tex]f:[a.b]→ℝ[/tex]

[tex]K(x,y)→[a,b]\times [a,b]→ℝ[/tex]

Is [tex][a,b]\times [a,b][/tex] Deckart product? Is that the way to construct [tex]ℝ^2[/tex] space?

If I say [tex]f\in C([a,b])[/tex], [tex]K\in C([a,b]\times [a,b])[/tex] that means that [tex]f[/tex] and [tex]K[/tex] are differentiable on this intervals. Right?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Defining of function in equation

**Physics Forums | Science Articles, Homework Help, Discussion**