We propose a new nonparametric approach in the field of Conformal Prediction based on a new family of nonconformity measures inducing conformal predictors able to create closed-form finite-sample valid or exact prediction sets for functional data under very minimal distributional assumptions. Our proposal ensures that the prediction sets obtained are bands, an essential feature in the functional setting that allows the viualization and interpretation of such sets. The procedure is also fast, scalable, does not rely on functional dimension reduction techniques and allows the user to select different nonconformity measures depending on the problem at hand always obtaining valid bands. Within this family of measures, we propose also a specific measure leading to prediction bands asymptotically no less efficient than those with constant width.