Linear Operators: Spectral theory |
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Page 853
... theory of spectral operators and the discussion of nonselfadjoint differential boundary value problems have been postponed for inclusion in the forthcoming Part III of this treatise . Since Part II deals ... spectral theorem for unbounded.
... theory of spectral operators and the discussion of nonselfadjoint differential boundary value problems have been postponed for inclusion in the forthcoming Part III of this treatise . Since Part II deals ... spectral theorem for unbounded.
Page 856
... Spectral Theorem for Unbounded Self Adjoint Operators 1191 3. Spectral Representation of Unbounded Self Adjoint Trans- formations 4. The Extensions of a Symmetric Transformation 5. Semi - bounded Symmetric Operators 6. Unitary Semi ...
... Spectral Theorem for Unbounded Self Adjoint Operators 1191 3. Spectral Representation of Unbounded Self Adjoint Trans- formations 4. The Extensions of a Symmetric Transformation 5. Semi - bounded Symmetric Operators 6. Unitary Semi ...
Page 1803
... Spectral theory . Bull . Amer . Math . Soc . 49 , 637–651 ( 1943 ) . Spectral theory I , Convergence to projections . Trans . Amer . Math . Soc . 54 , 185-217 ( 1943 ) . Integration and linear operations . Trans . Amer . Math . Soc . 40 ...
... Spectral theory . Bull . Amer . Math . Soc . 49 , 637–651 ( 1943 ) . Spectral theory I , Convergence to projections . Trans . Amer . Math . Soc . 54 , 185-217 ( 1943 ) . Integration and linear operations . Trans . Amer . Math . Soc . 40 ...
Contents
SPECTRAL THEORY Self Adjoint Operators in Hilbert Space | 858 |
BAlgebras | 859 |
Commutative BAlgebras | 868 |
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Common terms and phrases
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 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 PROOF prove real axis real numbers satisfies sequence solution spectral spectral theorem square-integrable subspace Suppose T₁ T₂ theory To(t topology tr(T unique unitary vanishes vector zero