The Spectral Representation of Ordinary Self-Adjoint Differential Operators
Earl A. Coddington · Annals of Mathematics · 1954
CODDINGTONThus R1T(V)= f TI(a) da.T(y)= fTI(a))T(7y)da= f Td(a-y)da.By the invariance of Haar measure the latter integral is merely R1.If R1 were a mapping from U into U, rather than from U into S, then as in the classical case (20) would imply that each T(a) is the identity.1 "Complex Spaces with Singularities," Ann.Math.(to appear).In the present note this paper will be referred to as "Complex Spaces."2Schwarz's lemma as given in "Complex Spaces" was formulated for single holo- morphic functions and is now being used for several simultaneously.