Linear operators. 2. Spectral theory : self adjoint operators in Hilbert Space |
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Page 1105
We have tr ( T ) = fr ( T ) , where fr ( T ) is the expression of Lemma 13 ( b ) . We now pause to sharpen another of the inequalities of Lemma 9 . 20 LEMMA . Let A , E C ,,, 4 , 6 C , A , C , ohere ' ++ 1.
We have tr ( T ) = fr ( T ) , where fr ( T ) is the expression of Lemma 13 ( b ) . We now pause to sharpen another of the inequalities of Lemma 9 . 20 LEMMA . Let A , E C ,,, 4 , 6 C , A , C , ohere ' ++ 1.
Page 1226
Part ( a ) follows immediately from Lemma 5 ( b ) , and part ( b ) follows immediately from part ( a ) and Lemma 5 ( c ) . Q.E.D. It follows from Lemma 6 ( b ) that any symmetric operator with dense domain has a unique minimal closed ...
Part ( a ) follows immediately from Lemma 5 ( b ) , and part ( b ) follows immediately from part ( a ) and Lemma 5 ( c ) . Q.E.D. It follows from Lemma 6 ( b ) that any symmetric operator with dense domain has a unique minimal closed ...
Page 1733
Q.E.D. Lemma 18 enables us to use the method of proof of Theorem 2 in the neighborhood of the boundary of a domain with ... 19 LEMMA . Let o be an elliptic formal partial differential operator of even order 2p , defined in a domain 1 ...
Q.E.D. Lemma 18 enables us to use the method of proof of Theorem 2 in the neighborhood of the boundary of a domain with ... 19 LEMMA . Let o be an elliptic formal partial differential operator of even order 2p , defined in a domain 1 ...
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additive adjoint operator algebra analytic assume B-algebra basis belongs Borel set boundary conditions boundary values bounded called clear closed closure commutative compact complex Consequently consider constant contains converges Corollary corresponding defined Definition denote dense determined eigenvalues element equal equation Exercise exists extension fact finite dimensional follows formal formal differential operator formula function function f given Hence Hilbert space Hilbert-Schmidt ideal identity independent inequality integral interval isometric isomorphism Lemma limit linear matrix measure multiplicity neighborhood norm normal operator obtained orthonormal positive preceding present projection proof properties prove range regular representation respectively restriction result satisfies seen sequence shown shows solution spectral spectrum square-integrable statement subset subspace sufficient Suppose symmetric Theorem theory topology transform uniformly unique unit unitary vanishes vector zero