Linear Operators: Spectral theory |
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Page 1801
... Math . Soc . 69 , 276-291 ( 1950 ) . Operations in Banach spaces . Trans . Amer . Math . Soc . 51 , 583–608 ( 1942 ) . Ergodic theorems for abelian semi - groups . Trans . Amer . Math . Soc . 51 , 399-412 ( 1942 ) . Strict convexity and ...
... Math . Soc . 69 , 276-291 ( 1950 ) . Operations in Banach spaces . Trans . Amer . Math . Soc . 51 , 583–608 ( 1942 ) . Ergodic theorems for abelian semi - groups . Trans . Amer . Math . Soc . 51 , 399-412 ( 1942 ) . Strict convexity and ...
Page 1817
... 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 equations ...
... 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 equations ...
Page 1878
... Math . 70 , 22–30 ( 1948 ) . Asymptotic integrations of the adiabatic oscillator in its hyperbolic range . Duke Math . J. 15 , 55-67 ( 1948 ) . On Dirac's theory of continuous spectra . Phys . Rev. 73 , 781-785 ( 1948 ) . - A new ...
... Math . 70 , 22–30 ( 1948 ) . Asymptotic integrations of the adiabatic oscillator in its hyperbolic range . Duke Math . J. 15 , 55-67 ( 1948 ) . On Dirac's theory of continuous spectra . Phys . Rev. 73 , 781-785 ( 1948 ) . - A new ...
Contents
BAlgebras | 859 |
Commutative BAlgebras | 868 |
Commutative BAlgebras | 874 |
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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 countably deficiency indices Definition denote dense eigenfunctions eigenvalues element equation essential spectrum Exercise exists f₁ finite dimensional follows from Lemma follows from Theorem formal differential operator formally self adjoint formula Fourier function f Haar measure Hence Hilbert space Hilbert-Schmidt operator homomorphism identity inequality infinity integral interval kernel L₁ L₁(R L₂ L₂(I L₂(R Lemma Let f linearly independent mapping matrix measure neighborhood non-zero norm operators in Hilbert orthogonal Plancherel's theorem positive preceding lemma prove real axis real numbers satisfies sequence shows solution spectral set spectral theorem square-integrable subset subspace Suppose T₁ T₂ theory To(t topology tr(T transform uniformly unique unitary vanishes vector zero