In Voisin's book on complex geometry, volume 1, page 128 she states that an elliptic differential operator is Fredholm. Her reference (Demailly 1996) is in French.
My question is: Is there a reference of this statement (with proof) in English or Russian?
An extra question: Voisin's treatment of differential operators is less than satisfactory (for me). If you could point out a reference for differential operators, the symbol of differential operators and a calculation of the symbol of the Laplacian, which is concise but illuminating, I would be very glad.