Linear Operators: Spectral operators |
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Page 1794
... spaces . A contribution to the theory of almost periodic functions . Acta ... Banach . C. R. Acad . Sci . Paris 206 , 1701–1704 ( 1938 ) . Éléments de ... Banach spaces . Amer . J. Math . 64 , 597–612 ( 1942 ) . 2. Linear topological ...
... spaces . A contribution to the theory of almost periodic functions . Acta ... Banach . C. R. Acad . Sci . Paris 206 , 1701–1704 ( 1938 ) . Éléments de ... Banach spaces . Amer . J. Math . 64 , 597–612 ( 1942 ) . 2. Linear topological ...
Page 1844
... Banach spaces . Duke Math . J. 13 , 351-365 ( 1946 ) . Introduction to measure and integration . Addison Wesley ... spaces L , and 1. Trans . Amer . Math . Soc . 41 , 138-152 ( 1937 ) . Quasi - complements and closed projections in ...
... Banach spaces . Duke Math . J. 13 , 351-365 ( 1946 ) . Introduction to measure and integration . Addison Wesley ... spaces L , and 1. Trans . Amer . Math . Soc . 41 , 138-152 ( 1937 ) . Quasi - complements and closed projections in ...
Page 1871
... Banach spaces . Doklady Akad . Nauk SSSR ( N. S. ) 52 , 569-572 ( 1946 ) . Concerning various forms of convergence of elements or linear operators in Banach spaces . Uspehi Matem . Nauk 1 , no . 5–6 ( 15-16 ) 228-229 ( 1946 ) ...
... Banach spaces . Doklady Akad . Nauk SSSR ( N. S. ) 52 , 569-572 ( 1946 ) . Concerning various forms of convergence of elements or linear operators in Banach spaces . Uspehi Matem . Nauk 1 , no . 5–6 ( 15-16 ) 228-229 ( 1946 ) ...
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 Haar measure 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 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 unique unitary vanishes vector zero