dtparekh
Member level 1
please can any one provide me the proofs!!!
Question:
Denote a vector space of all functions
f:R -> R
which are infinetly differentiable by C^∞(R). This space is called the space of smooth functions.
a. Show that C^∞ is infinite dimensional.
b. Show that differentiation is a linear transformation:
d/dx:C^∞(R)
c. For real number λ find an eigenvector for d/dx with eigen value λ[/b]
Question:
Denote a vector space of all functions
f:R -> R
which are infinetly differentiable by C^∞(R). This space is called the space of smooth functions.
a. Show that C^∞ is infinite dimensional.
b. Show that differentiation is a linear transformation:
d/dx:C^∞(R)
c. For real number λ find an eigenvector for d/dx with eigen value λ[/b]