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 \ f ( T ) | ≤1 whenever 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 \ f ( T ) | ≤1 whenever 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
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