Linear Operators: Spectral theory |
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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 ...
Page 1820
... Amer . Math . Soc . 46 , 959–962 ( 1940 ) . 2 . 3 . 4 . 5 . 6 . 7 . 8 . 9 . On uniform limitedness of sets of functional operations . Bull . Amer . Math . Soc . 29 , 309–315 ( 1923 ) . On bounded functional operations . Trans.Amer.Math ...
... Amer . Math . Soc . 46 , 959–962 ( 1940 ) . 2 . 3 . 4 . 5 . 6 . 7 . 8 . 9 . On uniform limitedness of sets of functional operations . Bull . Amer . Math . Soc . 29 , 309–315 ( 1923 ) . On bounded functional operations . Trans.Amer.Math ...
Page 1844
... Amer . Math . Soc . 52 , 167-174 ( 1946 ) . A second note on weak differentiability of Pettis integrals . Bull . Amer . Math . Soc . 52 , 668-670 ( 1946 ) . Müntz , Ch . H. 1 . Über den Approximationssatz von Weierstrass . Math ...
... Amer . Math . Soc . 52 , 167-174 ( 1946 ) . A second note on weak differentiability of Pettis integrals . Bull . Amer . Math . Soc . 52 , 668-670 ( 1946 ) . Müntz , Ch . H. 1 . Über den Approximationssatz von Weierstrass . Math ...
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 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 PROOF prove real axis satisfies sequence solution spectral spectral theorem square-integrable subset subspace Suppose T₁ T₁(t T₂ theory To(t topology tr(T unique unitary vanishes vector zero