Linear Operators: Spectral theory |
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Page 898
... identity for T. In order to relate this notion of the resolution of the identity with that given in Section 1 we state the following corollary . 6 COROLLARY . If E is the resolution of the identity for the normal operator T and if 8 is ...
... identity for T. In order to relate this notion of the resolution of the identity with that given in Section 1 we state the following corollary . 6 COROLLARY . If E is the resolution of the identity for the normal operator T and if 8 is ...
Page 920
... identity for T and Ĩ respectively . From Corollary 2.7 it is seen that E = = VEV - 1 and hence that ' ∞ F ( T ) = VF ( T ) V - 1 = for every bounded Borel function F. The mapping W UV of H onto -1 L2 ( ễn , μ ) is clearly an isometry ...
... identity for T and Ĩ respectively . From Corollary 2.7 it is seen that E = = VEV - 1 and hence that ' ∞ F ( T ) = VF ( T ) V - 1 = for every bounded Borel function F. The mapping W UV of H onto -1 L2 ( ễn , μ ) is clearly an isometry ...
Page 1717
... identity J1C ( x ) = JJ 3 C ( x ) J1 J2 + ( 1 ) JJ 2+ Σ J│ < │J2 + J2 with suitable coefficients CJ , J ,, holds ... identity ( 1 ) that Σ dj J2 ( X ) JT 1 JT 2 2 = Σ αγα ) . J1 = P1 , J2 = p | J | = 2p From this identity between ...
... identity J1C ( x ) = JJ 3 C ( x ) J1 J2 + ( 1 ) JJ 2+ Σ J│ < │J2 + J2 with suitable coefficients CJ , J ,, holds ... identity ( 1 ) that Σ dj J2 ( X ) JT 1 JT 2 2 = Σ αγα ) . J1 = P1 , J2 = p | J | = 2p From this identity between ...
Contents
BAlgebras | 859 |
Bounded Normal Operators in Hilbert Space | 887 |
Miscellaneous Applications | 937 |
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adjoint extension adjoint operator algebra analytic B-algebra B*-algebra Borel set boundary conditions boundary values bounded operator C₁ closed closure Co(I coefficients complex numbers converges Corollary deficiency indices Definition denote dense domain eigenfunctions eigenvalues element essential spectrum exists finite dimensional follows from Lemma follows from Theorem follows immediately formal differential operator formally self adjoint formula Fourier function defined function f Haar measure Hence Hilbert space Hilbert-Schmidt operator identity inequality integral interval kernel L₁(R L₂(I L₂(R Lemma Let f linearly independent mapping Math matrix measure neighborhood norm open set operators in Hilbert orthogonal orthonormal partial differential operator Plancherel's theorem positive preceding lemma prove real axis real numbers representation satisfies Section sequence solution spectral spectral theory square-integrable subspace Suppose symmetric operator T₁ T₂ theory To(t topology unique unitary vanishes vector zero