Linear Operators: Spectral theory |
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Page 927
... Riesz [ 20 , 6 ] which are quite modern in spirit . Many other proofs of the spectral theorem for self adjoint , unitary , or normal operators have been given , both in the bounded and unbounded cases . We refer the reader to the ...
... Riesz [ 20 , 6 ] which are quite modern in spirit . Many other proofs of the spectral theorem for self adjoint , unitary , or normal operators have been given , both in the bounded and unbounded cases . We refer the reader to the ...
Page 928
... Riesz [ 21 ] . Mimura [ 1 ] simplified Riesz's proof , and extended the result to unbounded operators . A more elementary proof was given by Sz . - Nagy [ 3 ; pp . 63-65 ] ( see also Riesz and Sz . - Nagy [ 1 ; Sec . 129 ] , Nakano [ 8 ...
... Riesz [ 21 ] . Mimura [ 1 ] simplified Riesz's proof , and extended the result to unbounded operators . A more elementary proof was given by Sz . - Nagy [ 3 ; pp . 63-65 ] ( see also Riesz and Sz . - Nagy [ 1 ; Sec . 129 ] , Nakano [ 8 ...
Page 1274
... Riesz and Sz . - Nagy [ 1 ; Sec . 141 ] and Sz . - Nagy [ 3 ; pp . 73-76 ] [ 14 ] . Stone's theorem has been extended to unitary representations of locally compact Abelian groups by Naimark [ 1 ] , Ambrose [ 4 ] , Godement [ 5 ] ...
... Riesz and Sz . - Nagy [ 1 ; Sec . 141 ] and Sz . - Nagy [ 3 ; pp . 73-76 ] [ 14 ] . Stone's theorem has been extended to unitary representations of locally compact Abelian groups by Naimark [ 1 ] , Ambrose [ 4 ] , Godement [ 5 ] ...
Contents
SPECTRAL THEORY Self Adjoint Operators in Hilbert Space | 858 |
BAlgebras | 859 |
Commutative BAlgebras | 868 |
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A₁ adjoint extension adjoint operator algebra analytic B-algebra Borel set boundary conditions boundary values bounded operator C₁ closed closure coefficients compact operator complex numbers continuous function converges Corollary deficiency indices Definition denote dense eigenvalues element equation essential spectrum Exercise exists finite dimensional follows from Lemma follows from Theorem follows immediately formal differential operator formally self adjoint formula Fourier function defined function f Hence Hilbert space Hilbert-Schmidt operator identity inequality integral interval isometric isomorphism kernel L₁ L₁(R L₂(I L₂(R Lemma Let f linear linearly independent mapping matrix measure neighborhood non-zero norm open set operators in Hilbert orthogonal orthonormal basis Plancherel's theorem positive preceding lemma prove real axis real numbers satisfies sequence solution spectral spectral theorem square-integrable subspace Suppose T₁ T₂ theory To(t topology transform unique unitary vanishes vector zero