Linear Operators, Part 2 |
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Results 1-3 of 41
Page 1343
... sufficiently close to 20 , o ( M ( 2 ) ) U is non - void . Thus if n ( 2 ) denotes the number of distinct points in the spectrum of M ( 1 ) , the sets { λ € σ \ n ( λ ) ≥ s } are relatively open in σ , and hence the sets b { λ € σ ...
... sufficiently close to 20 , o ( M ( 2 ) ) U is non - void . Thus if n ( 2 ) denotes the number of distinct points in the spectrum of M ( 1 ) , the sets { λ € σ \ n ( λ ) ≥ s } are relatively open in σ , and hence the sets b { λ € σ ...
Page 1449
... sufficiently large , then σ ( T ) is void . - ( d ) If q ( t ) → ∞ , if q is monotone decreasing for sufficiently large t , if ∞ q ( t ) ' ( q ( t ) ' ) 2 4 dt < ∞ \ q ( t ) | 5/2 ao for a sufficiently large , and ∞ Sono \ q ( t ) ...
... sufficiently large , then σ ( T ) is void . - ( d ) If q ( t ) → ∞ , if q is monotone decreasing for sufficiently large t , if ∞ q ( t ) ' ( q ( t ) ' ) 2 4 dt < ∞ \ q ( t ) | 5/2 ao for a sufficiently large , and ∞ Sono \ q ( t ) ...
Page 1694
... sufficiently large negative k . PROOF . Let C denote the compact carrier of F , and , using Lemma 2.2 , let o denote a function in Co ( I ) which is identically equal to one in a neighborhood of C. If our assertion is false , it follows ...
... sufficiently large negative k . PROOF . Let C denote the compact carrier of F , and , using Lemma 2.2 , let o denote a function in Co ( I ) which is identically equal to one in a neighborhood of C. If our assertion is false , it follows ...
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BAlgebras | 861 |
Commutative BAlgebras | 868 |
Commutative BAlgebras | 874 |
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adjoint extension adjoint operator algebra analytic B-algebra B*-algebra Borel set boundary conditions boundary values bounded operator C₁ closed closure coefficients compact operator complex numbers constant 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 subset subspace Suppose T₁ T₂ theory To(t topology unique unitary vanishes vector zero