Would someone be able to tell me what the dimension is of the following vector space?
The space consists of all $C^2$ functions $f: [a,b]\longrightarrow\mathbb{C}$ which, for pre-specified real $\alpha_1,\alpha_2,\beta_1,\beta_2$, meet the conditions:
\alpha_1f(a)-\alpha_2f'(a)=0,\qquad \beta_1f(b)-\beta_2f'(b)=0
I hope you can help. Thank you.