Kunze Linear Algebra · Problem 8.3.8

Inner Product Spaces

Mathematics — Methods · adjoints-polynomials

Problem

Let

V

be the vector space of the polynomials over

R

of degree less than or equal to 3, with the inner product

(f|g) = \int_0^1 f(t)g(t)\, dt.

t

is a real number, find the polynomial

g_t

V

such that

(f|g_t) = f(t)

for all

f

V