Linear Operators: Spectral theory |
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Page 1221
... measurable sets , and it follows that is u - measurable , completing the proof of statement ( i ) . От To complete the proof of the theorem , suppose that the functions W1 ( · , 2 ) , . . . , W2 ( · , λ ) are not linearly independent for u ...
... measurable sets , and it follows that is u - measurable , completing the proof of statement ( i ) . От To complete the proof of the theorem , suppose that the functions W1 ( · , 2 ) , . . . , W2 ( · , λ ) are not linearly independent for u ...
Page 1341
... measure u . If { m } is the matrix of densities of μ , with respect to μ , then there exist non- negative u - measurable functions q1 , i = 1 , ... , n , u - integrable over each bounded interval , and u - measurable functions a ,,, 1 ...
... measure u . If { m } is the matrix of densities of μ , with respect to μ , then there exist non- negative u - measurable functions q1 , i = 1 , ... , n , u - integrable over each bounded interval , and u - measurable functions a ,,, 1 ...
Page 5
... u is o - finite on 1 . page 172 , lines 14-17 : Delete these lines and ... measurable to integrable . Change ( E1 ( E2 ) to ( E1 ) ~ $ ( E2 ) . Change ... u - measurable . Let C ( p , x ) denote the closed cube with center p and side ...
... u is o - finite on 1 . page 172 , lines 14-17 : Delete these lines and ... measurable to integrable . Change ( E1 ( E2 ) to ( E1 ) ~ $ ( E2 ) . Change ... u - measurable . Let C ( p , x ) denote the closed cube with center p and side ...
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