Linear Operators: Spectral theory |
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Page 1260
... zero eigenvalues of T * T are the same as the non - zero eigenvalues of TT * , even as to multiplicity ( the positive square roots of these eigenvalues are sometimes called the characteristic numbers of T ) . 18 Let T be a bounded ...
... zero eigenvalues of T * T are the same as the non - zero eigenvalues of TT * , even as to multiplicity ( the positive square roots of these eigenvalues are sometimes called the characteristic numbers of T ) . 18 Let T be a bounded ...
Page 1419
... zero , f ' ( i + 1 ) 0. Since f ( t ) > 0 for s ; < t < 8¿ + 1 , f ' ( 8 ; +1 ) is negative . Thus f is negative ... zero , then it is bounded , and Theorem 23 applies to give the desired result . If q is negative for t sufficiently ...
... zero , f ' ( i + 1 ) 0. Since f ( t ) > 0 for s ; < t < 8¿ + 1 , f ' ( 8 ; +1 ) is negative . Thus f is negative ... zero , then it is bounded , and Theorem 23 applies to give the desired result . If q is negative for t sufficiently ...
Page 1727
... zero . Suppose that we let Io denote the cube I。= { x € E " || x , | ≤ 1 , i = 1 , ... , n } . Then for k ≤ min ... zero and if k ≤ min ( L ) ≤ max ( L ) ≤ k - 1 . In the same way we see , using ( 6 ) and ( 7 ) , that SL vanishes ...
... zero . Suppose that we let Io denote the cube I。= { x € E " || x , | ≤ 1 , i = 1 , ... , n } . Then for k ≤ min ... zero and if k ≤ min ( L ) ≤ max ( L ) ≤ k - 1 . In the same way we see , using ( 6 ) and ( 7 ) , that SL vanishes ...
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