Edelen D.G.B. Nonlocal variations and local invariance of fields

New York: American Elsevier, 1969. — 213 p.This is the first in a series of four papers dealing with the extensions of the Noether theorems on invariance and conservation laws to the nonlocal calculus of variations. After a summary of the germain aspects of the nonlocal variational calculus, the effects of the action of coordinate transformations and point transformations on the domain space of dependent functions are obtained. These results are then used to compute the variations in a functional of functionals that are induced by infinitesimal coordinate transformations and point transformations. Several forms are obtained for such variations since each will be required in the sequel.