Rational Solver
+1 vote
4 views
Let $V$ be the vector space of polynomials in the variable $t$ of degree at most 2 over $\mathbb{R}$. An inner product on $V$ is defined by

$$\langle f, g\rangle=\int_{0}^{1} f(t) g(t) d t$$

for $f, g \in V$. Let $W=\operatorname{span}\left\{1-t^{2}, 1+t^{2}\right\}$ and $\mathrm{W}^{\perp}$ be the orthogonal complement of $W$ in $V$. Which of the following conditions is satisfied for all $h \in W^{\perp}$?

1. $h$ is an even function, i.e. $h(t)=h(-t)$

2. $h$ is an odd function, i.e. $h(t)=-h(-t)$

3. $h(t)=0$ has a real solution

4. $h(0)=0$
in Functional Analysis by Expert (2.4k points) | 4 views

Please log in or register to answer this question.

Welcome to Rational Solver, where you can ask questions and receive answers from other members of the community.
49 questions
8 answers
1 comment
1,737 users