Linear Operators: Spectral theory |
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Page 1612
... apply . The more general theory of spectral operators , to be developed in Chapters XV , XVI , XVII and XVIII will ... application of perturbation methods to self adjoint operators , and thus will , in the last analysis , lean upon the ...
... apply . The more general theory of spectral operators , to be developed in Chapters XV , XVI , XVII and XVIII will ... application of perturbation methods to self adjoint operators , and thus will , in the last analysis , lean upon the ...
Page 1661
... apply to our new context we shall simply refer to " Lemma 6 , " etc. , as " generalized to D1 ( I ) " when necessary . Lemma 10 applies similarly in an evident way to the new situation , it being necessary to recall , however , XIV.3.30 ...
... apply to our new context we shall simply refer to " Lemma 6 , " etc. , as " generalized to D1 ( I ) " when necessary . Lemma 10 applies similarly in an evident way to the new situation , it being necessary to recall , however , XIV.3.30 ...
Page 1677
... Applying this to a F and noting that = π SF 4- ( FM - F ) , it follows that lim 4-1 ( Fo M1 - F ) | ( x ) 4 → 0 proving ( ii ) in case k≤0 . Q.E.D. 11 0 , 4 1 There is an important sense in which certain distributions may be taken to ...
... Applying this to a F and noting that = π SF 4- ( FM - F ) , it follows that lim 4-1 ( Fo M1 - F ) | ( x ) 4 → 0 proving ( ii ) in case k≤0 . Q.E.D. 11 0 , 4 1 There is an important sense in which certain distributions may be taken to ...
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