Linear Operators: Spectral theory |
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Page 1792
... Amer . Math . Soc . 9 , 373–395 ( 1908 ) . Existence and oscillation theorems for a certain boundary value problem . Trans . Amer . Math . Soc . 10 , 259–270 ( 1909 ) . Quantum mechanics and asymptotic series . Bull . Amer . Math . Soc ...
... Amer . Math . Soc . 9 , 373–395 ( 1908 ) . Existence and oscillation theorems for a certain boundary value problem . Trans . Amer . Math . Soc . 10 , 259–270 ( 1909 ) . Quantum mechanics and asymptotic series . Bull . Amer . Math . Soc ...
Page 1797
... Amer . J. Math . 78 , 289–309 ( 1956 ) . Algebras of certain singular operators . Amer . J. Math . 78 , 310–320 ( 1956 ) . Calkin , J. W. 1. Abstract symmetric boundary conditions . Trans . Amer . Math . Soc . 45 , 369-442 ( 1939 ) . 2 ...
... Amer . J. Math . 78 , 289–309 ( 1956 ) . Algebras of certain singular operators . Amer . J. Math . 78 , 310–320 ( 1956 ) . Calkin , J. W. 1. Abstract symmetric boundary conditions . Trans . Amer . Math . Soc . 45 , 369-442 ( 1939 ) . 2 ...
Page 1817
... Amer . J. Math . 76 , 831-838 ( 1954 ) . Hartman , P. , and Putnam , C. 1. The least cluster point of the spectrum of boundary value problems . Amer . J. Math . 70 , 847-855 ( 1948 ) . 2. The gaps in the essential spectra of wave ...
... Amer . J. Math . 76 , 831-838 ( 1954 ) . Hartman , P. , and Putnam , C. 1. The least cluster point of the spectrum of boundary value problems . Amer . J. Math . 70 , 847-855 ( 1948 ) . 2. The gaps in the essential spectra of wave ...
Contents
SPECTRAL THEORY Self Adjoint Operators in Hilbert Space | 858 |
BAlgebras | 859 |
Commutative BAlgebras | 868 |
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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 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(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 prove real axis real numbers satisfies sequence solution spectral spectral theorem square-integrable subspace Suppose T₁ T₂ theory To(t topology transform unique unitary vanishes vector zero