Linear Operators: Spectral theory |
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Page 1379
... neighborhood U of A , σ1 , ... , σ is a determining set for T. PROOF . If 0 ( ) is analytic for j > k , it follows from Theorem 18 that p ,, ( e ) = 0 for j > k and each Borel set e with compact closure contained in A. Thus , by Theorem ...
... neighborhood U of A , σ1 , ... , σ is a determining set for T. PROOF . If 0 ( ) is analytic for j > k , it follows from Theorem 18 that p ,, ( e ) = 0 for j > k and each Borel set e with compact closure contained in A. Thus , by Theorem ...
Page 1403
... neighborhood 4 such that W , ( ' , λ ) € L2 ( a , c ) for u , -almost all λ Д , since Д may then be written as a countable union of such neighborhoods A 。. We shall show below that for each e there exists a neighborhood 4 of 2 , an ...
... neighborhood 4 such that W , ( ' , λ ) € L2 ( a , c ) for u , -almost all λ Д , since Д may then be written as a countable union of such neighborhoods A 。. We shall show below that for each e there exists a neighborhood 4 of 2 , an ...
Page 1733
... neighborhood of the boundary of a domain with smooth boundary . This is carried out in the next two lemmas . 19 LEMMA . Let o be an elliptic formal partial differential operator of even order 2p , defined in a domain I。 of Euclidean n ...
... neighborhood of the boundary of a domain with smooth boundary . This is carried out in the next two lemmas . 19 LEMMA . Let o be an elliptic formal partial differential operator of even order 2p , defined in a domain I。 of Euclidean n ...
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