Linear Operators: Spectral theory |
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Page 1000
A similar argument shows that in ( z ) ▻ fy ( z ) uniformly on each compact subset on the half - plane I ( 2 ) > 0. If { In } were known to be uniformly convergent in a neighborhood of U , the analyticity of its limit fy would be clear ...
A similar argument shows that in ( z ) ▻ fy ( z ) uniformly on each compact subset on the half - plane I ( 2 ) > 0. If { In } were known to be uniformly convergent in a neighborhood of U , the analyticity of its limit fy would be clear ...
Page 1001
It is clear that in converges uniformly on any portion of Q whose closure contains neither a nor b . Let M be a bound for the sequence Yn so that M \ n ( a + is ) ] = M le - iax les -138 < 0 . 1s S $ * - * dx = In the same way it is ...
It is clear that in converges uniformly on any portion of Q whose closure contains neither a nor b . Let M be a bound for the sequence Yn so that M \ n ( a + is ) ] = M le - iax les -138 < 0 . 1s S $ * - * dx = In the same way it is ...
Page 1108
< Σ 12 il If 2 ; ( m ) is a parameter family of sequences such that ( i ) 2 ; ( m ) → h ; as m → 00 uniformly in i , ( ii ) lim - Lier 12 : ( m ) | * = 0 ) uniformly in m , , it follows that ( iii ) Lien 12 ; ( m ) / * is bounded ...
< Σ 12 il If 2 ; ( m ) is a parameter family of sequences such that ( i ) 2 ; ( m ) → h ; as m → 00 uniformly in i , ( ii ) lim - Lier 12 : ( m ) | * = 0 ) uniformly in m , , it follows that ( iii ) Lien 12 ; ( m ) / * is bounded ...
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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