Linear Operators: Spectral theory |
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Page 1012
... proof that HS is a B - space under the Hilbert - Schmidt norm . Finally , let T be in HS and let B be any bounded ... PROOF . It was seen during the proof of the theorem that HS is a subalgebra of B ( § ) , and the final paragraph of the ...
... proof that HS is a B - space under the Hilbert - Schmidt norm . Finally , let T be in HS and let B be any bounded ... PROOF . It was seen during the proof of the theorem that HS is a subalgebra of B ( § ) , and the final paragraph of the ...
Page 1179
... PROOF . We saw in the course of proving Theorem 25 that the mapping MK which sends a scalar - valued function with the Fourier transform f ( § ) into the vector - valued function whose nth component has the Fourier transform fn ...
... PROOF . We saw in the course of proving Theorem 25 that the mapping MK which sends a scalar - valued function with the Fourier transform f ( § ) into the vector - valued function whose nth component has the Fourier transform fn ...
Page 1459
... PROOF . We use the notations of the proof of Theorem 8. By Lemma 29 and Theorem 28 it is sufficient to show that t ' is finite below 10 in order to conclude that 7 is finite below 2. But it was shown in the proof of Theorem 8 that c may ...
... PROOF . We use the notations of the proof of Theorem 8. By Lemma 29 and Theorem 28 it is sufficient to show that t ' is finite below 10 in order to conclude that 7 is finite below 2. But it was shown in the proof of Theorem 8 that c may ...
Contents
BAlgebras | 859 |
Bounded Normal Operators in Hilbert Space | 887 |
Miscellaneous Applications | 937 |
Copyright | |
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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