Hilbert space methods in the theory of harmonic integrals

@article{Gaffney1955HilbertSM,
  title={Hilbert space methods in the theory of harmonic integrals},
  author={Matthew P. Gaffney},
  journal={Transactions of the American Mathematical Society},
  year={1955},
  volume={78},
  pages={426-444}
}
  • M. P. Gaffney
  • Published 1 February 1955
  • Mathematics
  • Transactions of the American Mathematical Society
The theory of harmonic integrals was created by Hodge [15], and the theorem which bears his name is the central result of the subject. Kodaira [17] and-independently-de Rham and Bidal [1] used the generalized harmonic operator A in their treatments of the theory. A was also used by Milgram and Rosenbloom [19] in their study of harmonic integrals with the heat equation. It is our purpose to develop the properties of A from the point of view of Hilbert space theory, thus arriving at Hodge's… 
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