Linear Operators: Spectral theory |
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Page 1196
... defined in Definition 1.1 or as in Definition VII.9.6 . This is the case , as will be shown in Corollary 8 below , so that the symbol f ( T ) for a polynomial ƒ is unambiguously defined . 6 THEOREM . Let E be the resolution of the ...
... defined in Definition 1.1 or as in Definition VII.9.6 . This is the case , as will be shown in Corollary 8 below , so that the symbol f ( T ) for a polynomial ƒ is unambiguously defined . 6 THEOREM . Let E be the resolution of the ...
Page 1548
... defined for the self adjoint operators T and ↑ as in Exercise D2 . Show that λ „ ( T ) ≥ λ „ ( Î ) , n ≥ 1 . 1 D11 Let T1 be a self adjoint operator in Hilbert space 1 , and let T2 be a self adjoint operator in Hilbert space 2. Define ...
... defined for the self adjoint operators T and ↑ as in Exercise D2 . Show that λ „ ( T ) ≥ λ „ ( Î ) , n ≥ 1 . 1 D11 Let T1 be a self adjoint operator in Hilbert space 1 , and let T2 be a self adjoint operator in Hilbert space 2. Define ...
Page 1647
... DEFINITION . Let 7 be a formal partial differential operator defined in an open subset I of E " , and with coefficients in C ( I ) . Let F be a distribution in I. Then TF will denote the distribution defined by the equation ( TF ) ( q ) ...
... DEFINITION . Let 7 be a formal partial differential operator defined in an open subset I of E " , and with coefficients in C ( I ) . Let F be a distribution in I. Then TF will denote the distribution defined by the equation ( TF ) ( q ) ...
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