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 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 |
Bounded Normal Operators in Hilbert Space | 887 |
Miscellaneous Applications | 937 |
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adjoint extension adjoint operator algebra analytic B-algebra B*-algebra Borel set boundary conditions boundary values bounded operator C₁ closed closure Co(I coefficients complex numbers converges Corollary deficiency indices Definition denote dense domain eigenfunctions eigenvalues element essential spectrum exists finite dimensional follows from Lemma follows from Theorem follows immediately formal differential operator formally self adjoint formula Fourier function defined function f Haar measure Hence Hilbert space Hilbert-Schmidt operator identity inequality integral interval kernel L₁(R L₂(I L₂(R Lemma Let f linearly independent mapping Math matrix measure neighborhood norm open set operators in Hilbert orthogonal orthonormal partial differential operator Plancherel's theorem positive preceding lemma prove real axis real numbers representation satisfies Section sequence solution spectral spectral theory square-integrable subspace Suppose symmetric operator T₁ T₂ theory To(t topology unique unitary vanishes vector zero