Linear Operators: Spectral theory |
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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 1698
Using Lemma 2.1 , let y be a function in C ( V ) with y ( x ) = 1 for x in K. Then , by Lemmas 3.22 and 3.10 , fovi = ylfonil ) = limm - ch , in the norm of H ( P ) ( V ) , so that in case ( a ) we have shown that focīt is the limit in ...
Using Lemma 2.1 , let y be a function in C ( V ) with y ( x ) = 1 for x in K. Then , by Lemmas 3.22 and 3.10 , fovi = ylfonil ) = limm - ch , in the norm of H ( P ) ( V ) , so that in case ( a ) we have shown that focīt is the limit in ...
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 ... 19 LEMMA . Let o be an elliptic formal partial differential operator of even order 2p , defined in a domain lo of ...
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 ... 19 LEMMA . Let o be an elliptic formal partial differential operator of even order 2p , defined in a domain lo of ...
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Contents
8 | 876 |
859 | 885 |
extensive presentation of applications of the spectral theorem | 911 |
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additive adjoint adjoint operator algebra analytic assume 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 domain eigenvalues elements equal equation equivalent Exercise exists extension fact finite dimensional follows follows from Lemma formal differential operator formula function given Hence Hilbert space Hilbert-Schmidt ideal identity immediately implies independent inequality integral interval invariant isometric isomorphism Lemma limit linear Ly(R mapping matrix measure multiplicity neighborhood norm obtained orthonormal positive preceding present projection proof properties prove range regular representation respectively restriction result satisfies seen sequence shown shows solutions spectral spectrum square-integrable statement subset subspace sufficient Suppose symmetric Theorem theory topology transform uniformly unique unit unitary vanishes vector zero