Linear Operators: Spectral theory |
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Page 853
... spectral theorem for self adjoint operators in Hilbert space . While there are some isolated discussions of ... theory of spectral operators and the discussion of nonselfadjoint differential boundary value problems have been postponed ...
... spectral theorem for self adjoint operators in Hilbert space . While there are some isolated discussions of ... theory of spectral operators and the discussion of nonselfadjoint differential boundary value problems have been postponed ...
Page 856
... Spectral Theorem for Unbounded Self Adjoint Operators 3. Spectral Representation of Unbounded Self Adjoint Trans- formations 1191 1205 4. The Extensions of a Symmetric Transformation . 1222 5. Semi - bounded Symmetric Operators . 1240 ...
... Spectral Theorem for Unbounded Self Adjoint Operators 3. Spectral Representation of Unbounded Self Adjoint Trans- formations 1191 1205 4. The Extensions of a Symmetric Transformation . 1222 5. Semi - bounded Symmetric Operators . 1240 ...
Page 1920
... 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 ) of an element in a B - algebra , IX.1.2 ...
... 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 ) of an element in a B - algebra , IX.1.2 ...
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