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 ) } zo is a strongly continuous semi - group with infinitesimal generator A * . 8 ( Cooper ) The infinitesimal generator of a strongly continuous ...
... semi - group of operators in Hilbert space with infinitesimal generator A , then { T * ( t ) } zo is a strongly continuous semi - group with infinitesimal generator A * . 8 ( Cooper ) The infinitesimal generator of a strongly continuous ...
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
BAlgebras | 859 |
Commutative BAlgebras | 868 |
Commutative BAlgebras | 874 |
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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 countably deficiency indices Definition denote dense eigenfunctions eigenvalues element equation essential spectrum Exercise exists f₁ finite dimensional follows from Lemma follows from Theorem formal differential operator formally self adjoint formula Fourier function f Haar measure Hence Hilbert space Hilbert-Schmidt operator homomorphism identity inequality infinity integral interval kernel L₁ L₁(R L₂ L₂(I L₂(R Lemma Let f linearly independent mapping matrix measure neighborhood non-zero norm operators in Hilbert orthogonal Plancherel's theorem positive preceding lemma prove real axis real numbers satisfies sequence shows solution spectral set spectral theorem square-integrable subset subspace Suppose T₁ T₂ theory To(t topology tr(T transform uniformly unique unitary vanishes vector zero