Linear Operators: Spectral theory |
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Page 1243
... semi - group are unitary operators on Hilbert space . 1 THEOREM . ( Stone ) If { U ( t ) , t≥ 0 } is a strongly continuous semi - group of unitary operators in Hilbert space , then there is a unique ( possibly unbounded ) self adjoint ...
... semi - group are unitary operators on Hilbert space . 1 THEOREM . ( Stone ) If { U ( t ) , t≥ 0 } is a strongly continuous semi - group of unitary operators in Hilbert space , then there is a unique ( possibly unbounded ) self adjoint ...
Page 1258
... semi - group of operators in Hilbert space with infinitesimal generator A , then { T * ( t ) } tzo is a strongly continuous semi - group with infinitesimal generator 4 * . 8 ( Cooper ) The infinitesimal generator of a strongly ...
... semi - group of operators in Hilbert space with infinitesimal generator A , then { T * ( t ) } tzo is a strongly continuous semi - group with infinitesimal generator 4 * . 8 ( Cooper ) The infinitesimal generator of a strongly ...
Page 1852
... semi - groups of linear transformations . Proc . Amer . Math . Soc . 2 , 234 ... group . Pacific J. Math . 5 , 269-283 ( 1955 ) . A decomposition of additive ... semi - ordered spaces . Doklady Akad . Nauk SSSR ( N. S. ) 55 , 379-381 ...
... semi - groups of linear transformations . Proc . Amer . Math . Soc . 2 , 234 ... group . Pacific J. Math . 5 , 269-283 ( 1955 ) . A decomposition of additive ... semi - ordered spaces . Doklady Akad . Nauk SSSR ( N. S. ) 55 , 379-381 ...
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