Linear Operators: Spectral theory |
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Page 1306
... second order operator 7 if 7 has no boundary values at a , and of limit circle type if 7 has two boundary values at a . The next theorem gives an important normal form for the boundary values of a second order real formally self adjoint ...
... second order operator 7 if 7 has no boundary values at a , and of limit circle type if 7 has two boundary values at a . The next theorem gives an important normal form for the boundary values of a second order real formally self adjoint ...
Page 1833
... second order . Trans . Amer . Math . Soc . 31 , 868-906 ( 1929 ) . LaSalle , J. P. 1 . 2 . Pseudo - normed linear spaces . Duke Math . J. 8 , 131–135 ( 1941 ) . Application of the pseudo - norm to the study of linear topological spaces ...
... second order . Trans . Amer . Math . Soc . 31 , 868-906 ( 1929 ) . LaSalle , J. P. 1 . 2 . Pseudo - normed linear spaces . Duke Math . J. 8 , 131–135 ( 1941 ) . Application of the pseudo - norm to the study of linear topological spaces ...
Page 1848
... second order . Doklady Akad . Nauk SSSR ( N.S. ) 85 , 41-44 ( 1952 ) . ( Russian ) Math . Rev. 14 , 473 ( 1953 ) . Investigation of the spectrum and expansion in eigenfunctions of singular non - self - adjoint differential operators of ...
... second order . Doklady Akad . Nauk SSSR ( N.S. ) 85 , 41-44 ( 1952 ) . ( Russian ) Math . Rev. 14 , 473 ( 1953 ) . Investigation of the spectrum and expansion in eigenfunctions of singular non - self - adjoint differential operators of ...
Contents
SPECTRAL THEORY Self Adjoint Operators in Hilbert Space | 858 |
BAlgebras | 859 |
Commutative BAlgebras | 868 |
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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 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