Linear Operators: Spectral theory |
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Page 888
... spectral measure in a B - space X. A spectral measure in X is a homomorphic map of a Boolean algebra of sets into a Boolean algebra of projection operators in X which has the additional property that it maps the unit in its domain into ...
... spectral measure in a B - space X. A spectral measure in X is a homomorphic map of a Boolean algebra of sets into a Boolean algebra of projection operators in X which has the additional property that it maps the unit in its domain into ...
Page 933
... spectral sets of von Neumann . If T is a bounded linear operator in a Hilbert space , then von Neumann [ 3 ] defines a closed set S of the complex sphere to be a spectral set of T if f ( T ) exists and \ ƒ ( T ) | ≤1 whenever f is a ...
... spectral sets of von Neumann . If T is a bounded linear operator in a Hilbert space , then von Neumann [ 3 ] defines a closed set S of the complex sphere to be a spectral set of T if f ( T ) exists and \ ƒ ( T ) | ≤1 whenever f is a ...
Page 1920
... Spectral asymptotics , XIII.10.G ( 1614 ) Spectral measure , X.1 ( 888 ) countably additive , X.I ( 889 ) self adjoint , X.I ( 892 ) Spectral multiplicity theory , defini- tion , X.5 ( 913 ) Spectral radius , definition , VII.3.5 ( 567 ) ...
... Spectral asymptotics , XIII.10.G ( 1614 ) Spectral measure , X.1 ( 888 ) countably additive , X.I ( 889 ) self adjoint , X.I ( 892 ) Spectral multiplicity theory , defini- tion , X.5 ( 913 ) Spectral radius , definition , VII.3.5 ( 567 ) ...
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