Linear Operators: Spectral theory |
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... S. 1 . 2 . 3 . 4 . 5 . 6 . 7 . 8 . Additive set functions on groups . Ann . Math . ( 2 ) 40 , 769-799 ( 1939 ) ... lp , n spaces . Amer . J. Math . 63 , 64–72 ( 1941 ) . Convex regions and projections in Minkowski spaces . Ann . of Math . ( 2 ) ...
... S. 1 . 2 . 3 . 4 . 5 . 6 . 7 . 8 . Additive set functions on groups . Ann . Math . ( 2 ) 40 , 769-799 ( 1939 ) ... lp , n spaces . Amer . J. Math . 63 , 64–72 ( 1941 ) . Convex regions and projections in Minkowski spaces . Ann . of Math . ( 2 ) ...
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