Linear Operators, Part 2 |
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... Theory IV . 3 Finite Dimensional Spaces VI . 2 Adjoints VIL4 Spectra of Compact Operators Extremal Points V1 . 10 Riesz Convexity Theorean VII . 6 Perturbation Theory VII1 . 8 Uniform Ergodic Theory VII . 9 Functions of Unbounded ...
... Theory IV . 3 Finite Dimensional Spaces VI . 2 Adjoints VIL4 Spectra of Compact Operators Extremal Points V1 . 10 Riesz Convexity Theorean VII . 6 Perturbation Theory VII1 . 8 Uniform Ergodic Theory VII . 9 Functions of Unbounded ...
Contents
BAlgebras | 859 |
Commutative BAlgebras | 868 |
Commutative BAlgebras | 874 |
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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 domain 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 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 tr(T transform unique unitary vanishes vector zero