Orthogonal Expansions of the Space of Vector Functions Which Are Square-Summable over a Given Domain and the Vector Analysis Operators

摘要

The Hilbert space L2(omega) of vector functions is studied. A breakdown of L2(omega) into orthogonal subspaces is discussed and the properties of the operators for projection onto these subspaces are investigated from the standpoint of preserving the differential properties of the vectors being projected. Finally, the properties of the operators are examined.